String Theory

In General > s.a. bosonic strings; phenomenology; String Field Theory.
* Idea: The theory of a 2D surface in a d-dimensional flat M, which can be thought of as a field theory on 2D Minkowski, the field being the metric induced on the world-sheet by d-dimensional Minkowski; For a realistic theory one needs to use superstrings, because bosonic strings have tachyons and no fermions.
* Motivation: It automatically includes "gravitons", and, in its supersymmetric version, gauge interactions, quark and lepton fields (more naturally than GUTS); It is thought to be finite (almost known to all orders), anomaly-free, and is the only known consistent theory of interacting particles of spin > 2; Has almost no free parameters (only the string tension), and only one fundamenta object.
* Problems: Vacuum non-uniqueness; Dependence of low-energy phenomenology on compactification scheme (no completely satisfactory model given yet); Vanishing of ; Divergent perturbation series (no renormalization needed, but the series is still asymptotic); Lack of underlying general principle; 1994, No known experimental signature.
* Goals: Search for non-metric string theory (in the spirit of topological field theories); Define the second-quantized theory (non-perturbative).
* History: The original phenomenological theory described hadrons as elongated strings, because of the long range forces indicated by the Regge trajectories; With strings considered as fundamental (anomaly cancellations), it became extremely popular in the mid-1980s, and made grandiose claims; Then decrease of interest (J Ehlers: It is in danger of losing contact with thought experiments!), until duality and M-theory came along.
* 4D strings: They are not really (geometrically) strings, but just theories with similar actions in 4D.

Superstrings
* Action: The area of the string in superspace, plus a Wess-Zumino term.
* Consistency: Consistent and well-behaved only in 10D, with gauge group SO(32) or E₈ × E₈ (496 generators).
* Types: There are five consistent types of string theories, Type I (unoriented, open or closed, admit only N = 1 supersymmetry); Type II (oriented, closed, with the N = 2 supersymmetry required for divergence cancellations–but in type II theories, gauge groups cannot be introduced by attaching quantum numbers to the ends of the strings); Heterotic (oriented closed, N = 1, made chiral by requiring left and right-moving excitations to be different; clockwise modes live in 10D with extra fermionic dimensions, while counterclockwise ones in a 26D bosonic space–the compactification of the extra 16 generates E₈ × E₈); and SO(32) (these groups are associated with the Yang-Mills charges).
* And phenomenology: The particles governed by the two E₈'s can have only gravitational interactions; Maybe we see only one group, the other one accounting for the missing mass.
@ References: Siegel NPB(86) [classical mechanics, Lagrangian and Hamiltonian]; Guttenberg a0807-PhD [general backgrounds].

References > s.a. history of physics; quantum spacetime; symplectic structures in general and in physics.
@ Articles: Green & Schwarz PLB(82), NPB(83), PLB(84), PLB(84) [anomaly-free], PLB(85) [likely finite]; Candelas, Horowitz, Strominger & Witten NPB(85); Gross, Harvey, Martinec & Rohm PRL(85), NPB(85), NPB(86) [E₈ × E₈ closed N = 1 heterotic]; Narain PLB(86).
@ I / II: Schwarz PT(87)nov; Davies & Brown 88; Linden PW(90)aug; Kaku 94; Bernstein 96; Duff SA(98)feb; Musser SA(98)oct; Greene pw(00)mar; Susskind pw(03)nov; Greene 03 [interview SA(03)nov]; Chalmers pw(07)sep; Cartwright & Frigg pw(07)sep; Gubser 10.
@ Books: Schwarz ed-85; Green, Schwarz & Witten 87; Polyakov 87; Brink & Henneaux 88; Freund & Mahanthappa ed-88; Friedan ed; Casati et al 91; Hatfield 92; Bailin & Love 94; Polchinski 98 [p05, solutions manual Headrick a0812]; Deligne et al 99 [for mathematicians]; Kaku 99; Szabo 04; Becker et al 07; Dine 07; Kiritsis 07; Becker et al 07; Zwiebach 09.
@ Intros, reviews: Schwarz PRP(82), in(85); Sen lecture notes; Horowitz in(86); Bailin CP(89); issue PTRS(89)#1605; Schwarz ht/96-in, ht/97; Dienes PRP(97); Kiritsis ht/97, ht/97-ln; Schwarz & Seiberg RMP(99)ht/98; Sen ht/98-in; Rudolph ht/98-ln; Álvarez & Meessen JHEP(99); Yoneya ht/00-in; Schwarz ht/00-MG9, hx/00-ln; Sen NPPS(01)ht/00; Mohaupt LNP(03)ht/02; de Boer ht/02-in; Schwarz ap/03-in [update]; Marolf AJP(04)jun-ht/03; Barbón EPJC(04)ht [ideas]; Johnson IJMPA(05); Krishnan ht/06-ln; Zapata ht/06; Schwarz ht/07-in, a0812-ln; Tseytlin a0808-ln; Belhaj a0808-ln; Sahoo EJP(09); Tong a0908-ln.
@ Quantization: Ohta PRD(86) [BRST]; Carlip & DeWitt-Morette PRL(88) [sign of the metric]; Grassi et al CQG(03) [covariant]; Tseytlin IJMPA(03) [semiclassical]; Guttenberg et al JHEP(04)ht [type II]; Grigore RVMP(07) [bosonic and supersymmetric strings].
@ Conceptual: Witten PTRS(89) [and higher symmetry]; Polyakov PAN(01)ht/00; Woit AS(02)phy/01; Marshakov PU(02)ht [motivation]; Witten ht/02-in [status]; Schnitzer phy/03 [history/philosophy of science]; Kim phy/04 [historical perspective].
@ Critical assessments: Larsson mp/01; Faraggi ht/03-in; Schroer IJMPD(08)phy/06, ht/06; Hedrich P&P-phy/06, JGPS(07)phy/06; Smolin 06; Woit 06; Emam AJP(08)jul-a0805; Schroer a0805; Zapata a0905 [results, acceptance, and AdS/cft]; Schroer a0906.
@ Nambu-Goto action: Grigore JPA(92); Ramos NPB(98) [reduced covariant phase space quantization]; > s.a. bosonic strings.
@ In curved space: Jain IJMPA(88); Viswanathan & Parthasarathy PRD(97); Sánchez IJMPA(03)ht-in; Orlando & Petropoulos ht/06-ln.
@ Background independence: Rahman ht/97, ht/97.
@ Uniqueness (including p-branes): Bars & Pope GRG(89).
@ And fundamental physics: Gibbs ht/96; Schlesinger FPL(02)ht/00, Brustein & de Alwis PRD(01) [universality].
@ In 4D: Dine ed-88; Meusburger & Rehren CMP(03)mp/02 [algebraic quantization of bosonic string]; Alexandre & Mavromatos ht/07.
@ Networks: Krogh & Lee NPB(98)ht/97; Sen JHEP(98)ht/97; Bhattacharyya et al PRL(98)ht [U-duality]; Verlinde & Vonk ht/03.
@ Substructure: Bergman ht/96, ht/96; Thorn ht/96.
@ Compactification: Reffert a0706-ln [geometric tools].
@ And loop space / spin networks: Ansoldi et al PRD(96), CQG(99); Starodubtsev gq/02; Sathiapalan IJMPA(03)ht/02; Mikovic ht/03; Mikovic ht/05-in [spin-foam formulation]; > s.a. bosonic strings.
@ Related topics: Álvarez NPB(83) [with boundaries]; Karliner et al IJMPA(88) [size, shape]; Shapiro & Taylor PRP(90) [spacetime supersymmetric]; 't Hooft NPB(90) [black hole interpretation]; Alvarez-Gaumé HPA(91) [random surfaces]; Witten ht/95; Gibbs ht/95 [and knots]; Hadasz & Rog PLB(96)ht [with particles at the ends]; Abel et al ht/99-in [thermodynamics]; Polchinski & Susskind ht/01 [hadron size]; Schreiber JHEP(04)ht, JHEP(04)ht [(super)-Pohlmeyer invariants]; Adam GRG(09) [perturbation theory].
> Related topics: see anomalies; cosmic strings; instantons; Moduli Space; non-commutative field theory.

Online Resources > s.a. The Official String Theory Website; Wikipedia article.
> Video clips: Discover clip of Brian Greene on String Theory in Two Minutes of Less.

"The unification of quantum mechanics and general relativity remains the primary goal of theoretical physics,
with string theory appearing as the only plausible unifying scheme." A Nicolaidis, arXiv:0812.1946

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