This page is a glossary of terms instring theory , including related areas such assupergravity ,supersymmetry , andhigh energy physics .
-bein A suffix indicating a frame, where the first part is a German word indicating the dimension (as in zweibein, vierbein, and so on). -ino The superpartners of bosons are often denoted by the suffix -ino; for example,photon /photino . s- The superpartners of fermions are often denoted by adding s- at the beginning; for example,quark /squark . α 1. Fine-structure constant 2. Regge slope , or inverse of thestring tension How are these related?There is only one dimensional constant in string theory, and that is the inverse string tensionα ′ {\displaystyle \alpha ^{\prime }} α ′ {\displaystyle \alpha ^{\prime }} l s = α ′ {\displaystyle l_{s}={\sqrt {\alpha ^{\prime }}}} 1 2 π α ′ . {\displaystyle {\frac {1}{2\pi \alpha ^{\prime }}}.} c = 1 {\displaystyle c=1} ℏ = 1 {\displaystyle \hbar =1} α ′ {\displaystyle \alpha ^{\prime }} ℏ {\displaystyle \hbar } α ′ {\displaystyle \alpha ^{\prime }} α ′ {\displaystyle \alpha ^{\prime }} α ( M 2 ) {\displaystyle \alpha (M^{2})} Regge theory is the derivative of spinS {\displaystyle S} d S d M 2 . {\displaystyle {\frac {dS}{dM^{2}}}.} p {\displaystyle p} c = 1 {\displaystyle c=1} S {\displaystyle S} α ′ {\displaystyle \alpha ^{\prime }} 1 / M 2 {\displaystyle 1/M^{2}} 3. A Fourier coefficient of a spacetime coordinate. 4. αs strong coupling constant β 1. One of the two conformal superghost fieldsβ ,γ used in the BRST quantization of the superstring 2. Euler beta function 3. Beta function describing the change of coupling constant under the renormalization group flow γ 1. Dirac matrix 2. One of the two conformal superghost fieldsβ ,γ used in the BRST quantization of the superstring 3. World-sheet metric γab 4. Photon 5. Euler constant .57721... Γ 1. Lattice 2. EulerGamma function 3. Dirac matrix 4. Width of some scattering process δ 1. Kronecker delta function 2. An infinitesimal change in something; for example δL is an infinitesimal change inL Δ 1. Propagator 2. Delta baryon , a baryon with 3 light quarks and isospin 3/2 3. Laplace operator in Euclidean space or more generally a Riemannian manifold ε 1. Small positive real number 2. Antisymmetric tensor η 1. Flat Lorentzian metric on spacetime 2. Dedekind eta function , a weight 1/2 modular form 3. Eta meson , a neutral flavor meson withP C = –+ θ 1. Theta function 2. θc is theCabbibo angle 3. θw is theWeinberg angle , also called the weak mixing angle Λ 1. Cosmological constant 2. Large energy or large mass cutoff in regularization 3. Lambda baryon , a baryon with 2 light quarks and isospin 0 μ 1. Renormalization scale, with the dimensions of mass 2. Muon ν Neutrino Ξ 1. Xi baryon , a baryon with 1 light quark π 1. 3.14159... 2. Pion Π The momentum density conjugate toX ρ Rho meson , a light meson with PC = ––σ 1. Spacelike coordinate on the world-sheet 2. Scattering cross section 3. Pauli matrix 4. See#sigma model Σ 1. Sigma baryon , a baryon with 2 light quarks and isospin 1 τ 1. Timelike coordinate on the world-sheet 2. Element of theupper half plane 3. Tauon Υ Upsilon meson (bb )φ Scalar field χ Neutral-flavor heavy meson with PC = ++ ψ 1. Spinor field 2. Psi meson (cc ) Ω 1. Density of something in the universe; for example, Ων is the neutrino density 2. Omega baryon , a baryon with no light quarks ' (prime) X ′ means ∂X /∂σ.dot above letter Ẋ means ∂X /∂τ ∇ 1. A covariant derivative 2. Thedel operator. □ TheD'Alembert operator , or non-Euclidean Laplacian. [,] A commutator: [A ,B ] =AB –BA . {,} An anticommutator: {A ,B } =AB +BA . A 1. A connection 1-form 2. Short for antiperiodic, a boundary condition on strings. 3. Short foraxial vector 4. An asymmetry action A functionS on the space of fields given (formally) by the integral of the Lagrangian density over spacetime, whose stationary points are the solutions of the equations of motion. ADE n n , E6 , E7 , E8 ) of simply lacedDynkin diagrams , and to several related classifications of Lie algebras, singularities and so on.ADHM Initials of Atiyah, Drinfeld, Hitchin, and Manin, as in theADHM construction of instantons. ADM Initials of Arnowitt, Deser, and Misner, as inADM energy , a way of defining the global energy in an asymptotically flat spacetime, orADM decomposition of a metric, orADM formalism . AdS Anti-de Sitter, as inanti-de Sitter space , a Lorentzian analogue of hyperbolic space AdS/CFT Anti-de Sitter/conformal field theory, especially theAdS/CFT correspondence . ALE Asymptotically locally Euclidean ALEPH ALEPH experiment at LEPAMSB Anomaly mediation supersymmetry breaking ASD Anti self-dual (connection) ATLAS TheATLAS experiment atCERN , a particle detector. axino axion strong CP problem .b 1. One of the two conformal ghost fieldsb ,c used in the BRST quantization of the bosonic string. 2. Abottom quark . B 1. Baryon number 2. Short forboson . 3. Short forbaryon . 4. Short for backward;for example, σB 5. abottom meson . BAO Baryon acoustic oscillation BB Big Bang BBN Big Bang nucleosynthesis bino BIon A BPS solution representing an infinite string ending on a D-brane. Named after theBorn–Infeld action . BPS Bogomol'nyi–Prasad–Sommerfield bound .BR Branching ratio BRS BRST quantization BRST quantization of gauge theories.brane Short for membrane. a higher-dimensional manifold moving in spacetime. See also p-brane, D-brane. BTZ Initials of Bañados–Teitelboim–Zanelli, as inBTZ black hole , a black hole in 2+1-dimensional gravity. BV Batalin–Vilkovisky, as inBatalin–Vilkovisky formalism . c 1. Thespeed of light , when not using units where this is 1. 2. A central charge of the Virasoro algebra or similar algebra. 3. One of the two conformal ghost fieldsb ,c used in the BRST quantization of the bosonic string. 4. AChern class . 5. Acharm quark . C 1. Charge, especially thecharge symmetry . Calabi–Yau Kähler manifold with vanishingRicci curvature , used for compactifying string theories.CAR Canonical anticommutation relations CBR Cosmic background radiation CC 1. Charged current (weak interaction). 2. Complex conjugate 3. Compatibility condition CCR Canonical commutation relation CCR and CAR algebras CDF Collider Detector at Fermilab CDM Cold dark matter CERN Conseil Européen pour la Recherche Nucléaire chargino gauge boson .Chern–Simons 1. 2. chiral 1. Not invariant under the parity symmetry. The word comes from the Greek χειρ meaning "hand"; the terms "left-handed" and "right-handed" are often used to describe chiral objects. 2. Achiral multiplet is a type of supermutliplet of a supersymmetry algebra. CIPT Contour improved perturbation theory CKG Short for conformal Killing group. CKM TheCabibbo–Kobayashi–Maskawa matrix . CKS Short for conformal Killing spinor. CKV Short for conformalKilling vector . CFT Conformal field theory Chan–Paton AChan–Paton charge is a degree of freedom carried by an open string on its endpoints. cl 1. Short for classical (for example,S cl 2. CL is short for confidence limit. closed A closed string is one with no ends. CM Center of mass (frame) CMB CMBR Cosmic microwave background radiationCMS 1. TheCompact Muon Solenoid atCERN , a particle detector. 2. Short for the Center-of-Momentum System, a coordinate system where the total momentum is 0. compactification A method for reducing the apparent dimension of spacetime by wrapping the string around a compact manifold. cosmological constant CP Short for Charge–Parity, as inCP symmetry . CPC Short for Charge–Parity conservation. CPT Short for Charge–Parity–Time, as inCPT symmetry orCPT theorem . CPV Short for Charge–Parity violation. critical Thecritical dimension is the spacetime dimension in which a string or superstring theory is consistent; usually 26 for string theories and 10 for superstring theories. CVC Conservedvector current . CY Short for Calabi–Yau, as inCalabi–Yau manifold , a Ricci-flat Kähler manifold, often used for compactifying superstring theories. d 1. Theexterior derivative of a form. 2. Adown quark . 3. The dimension of spacetime. D 1. Short for Dirichlet, as in D-brane 2. The dimension of spacetime 3. A connection or differential operator 4. ADynkin diagram of an orthogonal group in even dimensions. 5. Acharmed meson . D0 D-brane Dp-brane p +1) on which the ends of strings are constrained to lie, so that the strings satisfy Dirichlet boundary conditions.D-string A D1-brane DBI Short for Dirac–Born–Infeld, as in theDBI action , an action based on theBorn–Infeld action , a modification of the Maxwell action of electrodynamics. DDF Initials of Del Guidice, Di Vecchia, and Fubini, as inDel Guidice–Di Vecchia–Fubini operator , operators generating an oscillator algebra. DELPHI DELPHI experiment at LEP.DESY Deutsches Elektronen-Synchrotron DGLAP Initials of Dokshitzer–Gribov–Lipatov–Altarelli–Parisi who introduced theDGLAP evolution equation in QCD. Diff Diffeomorphism ordiffeomorphism group .dilatino dilaton Dirichlet Dirichlet boundary conditions on an open string say that the ends of the string are fixed (often lying on a D-brane).DIS Deep inelastic scattering DLCQ Discrete light-cone quantization DM Dark matter DØ Dp-brane p +1) on which the ends of strings are constrained to lie, so that the strings satisfy Dirichlet boundary conditions.DR 1. Short fordimensional regularization . 2. Short fordimensional reduction , a way of constructing theories from simpler theories in higher dimensions, sometimes by making fields invariant under some spacelike translations. dS de Sitter, as inde Sitter space , a Lorentzian analogue of a sphere dS/CFT de Sitter/conformal field theory, especially thedS/CFT correspondence . dual resonance model duality S-duality ,T-duality ,U-duality ,mysterious duality .DY Initials of Drell–Yan, as inDY process . dyon e 1. Euler's constant 2. A frame 3. An electron E Energy E6 6 is the exceptional Lie algebra of rank 6 and dimension 78.E7 7 the exceptional Lie algebra of rank 7 and dimension 133.E8 8 the exceptional Lie algebra of rank 8 and dimension 248.eff Short for effective (field theory). EFT Effective field theory , a low-energy approximation to a theory.einbein A frame in 1 dimension elfbein A frame in 11 dimensions energy–momentum tensor T (also called the stress-energy tensor) describing the variation of the action under changes in the metric, whose components give the local energy, momentum and stress densities. In flat spacetimes it can also be given by combining the Noether currents of the translation symmetries.EWSB Electro-weak symmetry breaking. F 1. Acurvature form of a connection 2. The world-sheetfermion number . 3. Short for fermion 3. Short for forward;for example, σF F4 4 is the exceptional Lie algebra of rank 4 and dimension 52.FCNC Flavor-changingneutral current . field A section of a fiber bundle FOPT Fixed-order perturbation theory. F-string Fundamental string F-theory FRW Friedman–Robertson–Walker metric on spacetimeg 1. A metric 2. A coupling constant 3. Thegenus of a Riemann surface . 4. Agluon . G 1. Newton'sgravitational constant , sometimes writtenG N 2. TheFermi coupling constant for weak interactions, sometimes writtenG F 3. G n G2 G2 manifold with G2 holonomy.gaugino A spin 1/2 supersymmetric partner of a gauge boson. gh Abbreviation for ghost; for example,S gh ghost A vector of negative norm. GKO Short for Goddard–Kent–Olive. The GKO construction, also called thecoset construction , is a way of constructing unitary discrete series representations of the Virasoro algebra. GL Ageneral linear group . gluino gluon .gluon gauge boson associated with thestrong force .GMSB Gauge mediated supersymmetry breaking. goldstino Goldstone boson .GR General relativity graviton gravitino Green Named forMichael Green . GS Green–Schwarz formalism, a way of incorporating supersymmetry into string theory that is supersymmetric in 10-dimensional spacetime. GSO Short for Ferdinando Gliozzi, Joël Scherk, and David A. Olive, as in theGSO projection , a projection in superstring theory that eliminates tachyons. GSW The 2-volume work on superstring theory by Green, Schwarz, and Witten. GUT Grand Unified Theory , a hypothetical theory unifying the strong and electroweak forces.GWS Glashow–Weinberg–Salem theory of theelectroweak force . GZK TheGreisen–Zatsepin–Kuzmin limit on the energy of cosmic background radiation from distant sources. h 1. The weight of a field (for example, its eigenvalue forL 0 ). 2. Hermitian; for example, h.c. stands form hermitian conjugate. H 1. TheHamiltonian . 2. TheHiggs boson . 3. TheHubble constant . Haag–Łopuszański–Sohnius theorem Coleman–Mandula theorem .Hagedorn temperature h.c. hc Hermitian conjugate HCMS Hadronic center of mass (frame) HDM Higgs doublet model HE Short for heterotic-E2 8 2 8 helicity HERA Hadron Elektron Ring Anlage heterotic heterosis , meaning hybrid vigour. A hybrid of bosonic string theory and superstring theory, introduced by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm in 1985.Higgs boson Higgsino Higgs boson .HO Short for heterotic-orthogonal, a heterotic string theory based on the orthogonal group O32 (R ). holographic principle HQET Hyperkähler Hyperkaehler Hypermultiplet i √–1 I Isospin .IGM Intergalactic medium inflation instanton int Short for interaction; for example,H int might be an interaction Hamiltonian. inv Short for invisible; for example, Γinv is the width for invisible decays (those unobseverd by an experiment). J 1. A current 2. A source 3. Spin. k A momentum K Akaon (a strange meson). K3 Kodaira dimension 0K-theory Kac–Moody algebra loop algebra .Kähler Kaehler Named afterErich Kähler 1. AKähler manifold is a complex manifold with a compatible Riemannian metric. 2. AKähler metric is the metric on a Kähler manifold. 3. AKähler potential is a function of superfields used to construct a Lagrangian. Kalb–Ramond field KK Kaluza–Klein KM 1. TheKobayashi–Maskawa mechanism for CP violation. 2. Kac–Moody algebra . KZ Initials of Knizhnik and Zamolodchikov, as inKZ equation , a differential equation related to the primary fields of a current algebra. L 1. ALagrangian 2. L n Virasoro algebra . 3. An abbreviation for left (moving modes) 4. Lepton number 5. Short for lepton L3 L3 experiment at LEP.Lagrangian (field theory) landscape LEP TheLarge Electron–Positron Collider at CERN. lepton LH Left-handed LHC TheLarge Hadron Collider atCERN . little string theory LL Double logarithmic LO Leading order (term)LQG Loop quantum gravity LQC Loop quantum cosmology LSP Abbreviation forlightest supersymmetric particle . LSS Large scale structure (of the universe). m A mass of a fermion. For example,m t t . M The mass of a boson; for example,M Z Majorana fermion Majorana spinor Majorana–Weyl fermion Majorana–Weyl spinor Mandelstam variable matrix theory M(atrix) theory M-brane membrane MC Monte Carlo integration MCG minimal model Certain solvableconformal field theories . Mirror symmetry (string theory) MLLA Modified leading logarithm approximation. MNS Maki–Nakagawa–Sakata matrix for neutrino mixingmonopole Montonen–Olive duality S-duality .MS minimal subtraction (a renormalization scheme).MS is themodified minimal subtraction scheme .MSM Abbreviation forminimal standard model . MSSM Abbreviation forminimal supersymmetric standard model . mSUGRA Minimal model of supergravity .M-theory MSW Mikheyev–Smirnov–Wolfenstein effect concerning neutrino oscillations in matter.multiplet A linear representation of a Lie algebra or group. A collection of elementary particles corresponding to a basis of a representation. N 1. The number of times each irreducible real spinor representation appears in the fermionic part of asupersymmetry algebra orsuper Minkowski space . It is often used in the description of anextended supersymmetry algebra, as inN=2 superconformal algebra and so on. 2. Anucleon , a baryon with 3 light quarks and isospin 1/2 (such as aproton orneutron ). 3. The number of some type of particle. Nambu–Goto action NC Neutral current (weak interaction). Neumann Neumann boundary conditions on an open string say that the momentum normal to the boundary of the world-sheet is zero.neutralino gauge boson with zero charge.Neveu Named forAndré Neveu . Neveu–Schwarz algebra Virasoro algebra , similar to theRamond algebra .NG 1. Short for Nambu–Goto, as inNambu–Goto action . 2. Short for Nambu–Goldstone, as inNambu–Goldstone boson . NLL Next to leading logarithmic (term). NLO Next to leading order (term). NLSP next-to-lightest sypersymmetric particle NMSSM Next-to-Minimal Supersymmetric Standard Model .NNLL Next to next to leading logarithmic (term). NNLO Next to next to leading order (term). NNNLL Next to next to next to leading logarithmic (term). no-ghost theorem no-go theorem .NR Non-relativistic NRQCD Non-relativistic quantum chromodynamics NS Neveu–Schwarz, especially theNeveu–Schwarz algebra NS–NS A sector with Neveu–Schwarz conditions on left and right moving modes. NS–R A sector with Neveu–Schwarz conditions on left moving modes and Ramond conditions on right moving modes. NUT The initials of E. Newman, L. Tamburino, and T. Unti, mainly used inTaub–NUT vacuum , a solution to Einsteins' equations. O Anorthogonal group OCQ Short for old covariant quantization OPAL TheOPAL detector at LEP. open An open string is one with two ends. OPE operator product expansion orbifold OSp ALie superalgebra . p A momentum P 1. Parity, especially theparity symmetry . 2. Short for periodic, a boundary condition on strings (as opposed to A for antiperiodic). 3. Pseudoscalar (current) 4. Momentum 5. One of the bosonic elements of asupersymmetry algebra . p -braneAp +1 dimensional membrane, wherep is a non-negative integer. The dimension of membranes is often given by their space dimension, which is 1 less than their full spacetime dimension. PCAC partially conserved axial vector current PDF Parton distribution function .PDG Particle Data Group .photino photon PMNS Pontecorvo–Maki–Nakagawa–Sakata matrix for neutrino mixingPolyakov action PQ Peccei–Quinn, as inPeccei–Quinn theory . pQCD PQCD Perturbativequantum chromodynamics . prepotential A function used to construct the vector superfield insupersymmetric gauge theory andSeiberg–Witten theory . primary field A field killed by the positive weight operators of the Virasoro algebra (or similar algebra); in other words, a lowest weight vector. Princeton string quartet David Gross ,Jeffrey Harvey ,Emil Martinec , andRyan Rohm , who introduced theheterotic string in 1985.PSL Projective special linear group .q Aquark . Q 1. TheBRST operator . 2. A charge 3. One of the fermionic generators of asupersymmetry algebra . quark QCD QED R 1. Short for Ramond, as inRamond sector . 2. A curvature tensor 3. An abbreviation for right (moving modes). 4. A radius 5. R-symmetry is a symmetry ofextended supersymmetry algebras. Ramond Named forPierre Ramond . Ramond algebra Virasoro algebra , similar to theNeveu–Schwarz algebra .Rarita–Schwinger Regge 1. PhysicistTullio Regge . 2. Regge trajectory : the squared mass of a hadronic resonance is roughly linear in the spin, with the constant of proportionality called theRegge slope . revolution Any new idea in string theory. In particular thefirst superstring revolution refers to the discoveries in the mid 1980s such as the cancellation of gravitational anomalies and theheterotic string , and thesecond superstring revolution refers to the discoveries in the mid 1990s, such asD-branes ,M-theory , and matrix theory and theAdS/CFT correspondence . RG Renormalization group .RGE Renormalization group equation.RH Right-handed R–NS A sector with Ramond conditions on left moving modes and Neveu–Schwarz conditions on right moving modes. RNS Ramond–Neveu–Schwarz, as inRNS formalism , a way of incorporating supersymmetry into string theory that is supersymmetric on the world sheet. R-parity Z 2 symmetry of supersymmetric models.R-R Short forRamond–Ramond sector s 1. Astrange quark . 2. AMandelstam variable S 1. An action 2. Ascattering matrix . 3. The transformation τ → –1/τ of the upper half plane 4. Scalar (current) 5. Short forsuper orsupersymmetric S-brane A brane similar to a D-brane, with Dirichlet boundary conditions in the time direction. S-duality string duality relating theories with a large coupling constant to theories with a small coupling constantSBB StandardBig Bang model of the universe SCFT Superconformal field theory , a supersymmetric extension of conformal field theorySchwarz Named forJohn Henry Schwarz Seiberg duality SGA Abbreviation forSpectrum-generating algebra short supermultiplet A supermultiplet (representation) related toBPS states sigma model SL Special linear group SLAC Stanford Linear Accelerator Center SLC Stanford Linear Collider slepton SM sneutrino SO Special orthogonal group Sp Symplectic group sphaleron squark SSB Spontaneous symmetry breaking SSM Standard solar model stress–energy tensor Alternative name for the#energy–momentum tensor . string field theory SU Special unitary group SUGRA Short forsupergravity superconformal algebra superfield supergravity supermultiplet supersymmetry algebra superpotential superspace superstring supersymmetry Lie superalgebra , where the Lie bracket [a ,b ] is sometimes given byab +ba rather thanab –ba .SUSY An abbreviation forsupersymmetry . SYM Supersymmetric Yang–Mills t 1. Atop quark . 2. AMandelstam variable . 3. Time. T 1. Theenergy–momentum tensor . 2. Time, especially thetime symmetry . 3. The transformation τ → τ+1 of the upper half plane. 4. A torus. 5. The string tension. 6. Temperature. 7. Tensor (current) T-duality string duality relating theories on a large spacetime to theories on a small spacetime. In particular it exchanges type IIA and IIB superstring theory.tachyon ToE TOE Theory of everything type I type II type IIA type IIB d =10 supersymmetries, and types IIA or IIB are distinguished by whether the supersymmetries of left and right movers have opposite or identical chiralities.u 1. Anup quark . 2. AMandelstam variable . U Aunitary group . U-duality string duality relating two different string theories.UED Universal extra dimensions UV Short for ultra-violet, often referring to short-distance singularities. V 1. Avertex operator . 2. Vector (current) V-A Vector-Axial vector vector superfield A type ofsuperfield related tovector supermultiplets . VEV Vacuum expectation value of an operator.vielbein A frame vierbein A frame in 4 dimensions. Sometimes used for a frame in an arbitrary number of dimension by authors who do not care that "vier" means four in German. Veneziano amplitude Euler beta function interpreted as a scattering amplitude.vertex operator Virasoro algebra Witt algebra of polynomial vector fields on a circle.w A complex number W AW-boson W-algebra Weyl 1. Named afterHermann Weyl 2. AWeyl transformation is a rescaling of the world-sheet metric. 3. Weyl spinor , an element of a half-spin representation in even spacetime dimensions. WIMP Weakly interacting massive particle wino W-boson .Witten Named forEdward Witten . WMAP Wilkinson Microwave Anisotropy Probe world sheet The 2-dimensional subset of spacetime swept out by a moving string. world-volume Thep +1-dimensional spacetime volume swept out by ap -brane, as in world-volume action. WZNW WZW Initials of Wess, Zumino, (Novikov), and Witten, as in theWZW model , a σ-model with a group as the target space. x A real number X Used for coordinates in Minkowski space. y A real number YBE Yang–Baxter equation YM Yang–Mills z A complex number Z 1. A partition function 2. TheZ boson . An element of the center of anextended supersymmetry algebra . ZEUS zino zweibein A frame in 2 dimensions Becker, Katrin,Becker, Melanie , andJohn H. Schwarz (2007)String Theory and M-Theory: A Modern Introduction . Cambridge University Press.ISBN 0-521-86069-5 Binétruy, Pierre (2007)Supersymmetry: Theory, Experiment, and Cosmology . Oxford University Press.ISBN 978-0-19-850954-7 Dine, Michael (2007)Supersymmetry and String Theory: Beyond the Standard Model . Cambridge University Press.ISBN 0-521-85841-0 Paul H. Frampton (1974).Dual Resonance Models . Frontiers in Physics.ISBN 0-8053-2581-6 Michael Green ,John H. Schwarz andEdward Witten (1987)Superstring theory . Cambridge University Press. The original textbook.Kiritsis, Elias (2007)String Theory in a Nutshell . Princeton University Press.ISBN 978-0-691-12230-4 Johnson, Clifford (2003).D-branes . Cambridge: Cambridge University Press.ISBN 0-521-80912-6 Polchinski, Joseph (1998)String Theory . Cambridge University Press.Szabo, Richard J. (Reprinted 2007)An Introduction to String Theory and D-brane Dynamics . Imperial College Press.ISBN 978-1-86094-427-7 Zwiebach, Barton (2004)A First Course in String Theory . Cambridge University Press.ISBN 0-521-83143-1 
