String
Theory |

**In General** > s.a. bosonic
strings; history
of particle physics; string 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 has no ultraviolet divergences and is thought to be finite (this is almost known to all orders),
anomaly-free,
and is the only known consistent theory of interacting particles of spin >
2; It has almost no free parameters (only the string tension), and only one fundamental
object.

* __Problems__: Vacuum non-uniqueness;
Dependence of low-energy phenomenology on the compactification scheme (no completely
satisfactory model is known yet); Vanishing
of the cosmological constant; Divergent
perturbation series (no renormalization is 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).

* __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 E_{8} × E_{8} (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 E_{8} ×
E_{8});
and SO(32) (these groups are associated with the Yang-Mills charges).

* __And phenomenology__:
The particles governed by the two E_{8}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 PhD(07)-a0807
[general backgrounds].

**Other Types of Strings**

* __Ambitwistor string theories__: A family of chiral (holomorphic) string theories whose target space is the space of complexified null geodesics in a general spacetime; Like conventional strings, they are critical in 10 dimensions and describe supergravity, but unlike conventional strings, they do not admit a tower of higher massive modes (and are correspondingly not thought to be ultraviolet finite).

@ __References__:
Álvarez NPB(83)
[with boundaries]; Shapiro & Taylor PRP(90)
[spacetime supersymmetric]; Hadasz & Rog PLB(96)ht [with
particles at the ends]; Geyer et al CQG(15) & CQG+(15) [ambitwistor strings].

**References** > s.a. non-local theories; 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)
[E_{8} ×
E_{8} closed *N* = 1 heterotic]; Narain
PLB(86); Susskind FP(13); Duff FP(13) [response to critics]; Polchinski a1512-conf [unification of quantum mechanics and general relativity].

@ __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; Conlon 15.

@ __Books__: Schwarz ed-85; Green, Schwarz & Witten 87; Polyakov 87;
Brink & Henneaux 88; Freund & Mahanthappa ed-88; Hatfield 92; Bailin & Love 94; Polchinski 98 [solutions
manual Headrick a0812];
Kaku 99;
Becker et al 07; Kiritsis 07; Zwiebach 09; Szabo 11; West 12; Dine 16; in Manoukian 16; Schomerus 17.

@ __Intros, reviews__: Schwarz PRP(82),
in(85); Sen lecture notes; Horowitz in(86);
Bailin CP(89);
issue PTRS(89)#1605;
Schwarz ht/96-conf, ht/97;
Dienes PRP(97);
Kiritsis ht/97,
ht/97-ln;
Schwarz & Seiberg RMP(99)ht/98;
Sen ht/98-proc;
Rudolph ht/98-ln; Álvarez & Meessen
JHEP(99);
Yoneya ht/00-conf;
Schwarz ht/00-MG9,
hx/00-ln;
Sen NPPS(01)ht/00;
Mohaupt LNP(03)ht/02;
de Boer NPPS(03)ht/02;
Schwarz ap/03-conf
[update]; Marolf AJP(04)jun-ht/03;
Barbón EPJC(04)ht [ideas];
Johnson IJMPA(05);
Krishnan ht/06-ln;
Zapata ht/06;
Schwarz PTPS(07)ht, IJMPA(10)-a0812-ln; Tseytlin
a0808-ln; Belhaj a0808-ln;
Sahoo EJP(09);
Tong a0908-ln; Bedford a1107-ln; Mukhi CQG(11)-a1110 [25 years]; Stelle LNP(13)-a1203; issue FP(13)#1; Witten PT(15)nov [what every physicist should know].

@ __And mathematics__: Deligne et al 99 [string theory for mathematicians]; > s.a. finite groups [monshine]; mathematical physics [relationship].

@ __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]; > s.a. renormalization.

@ __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]; Johansson & Matsubara SHPMP(11)-a0912 [philosophical
perspective]; Rickles FP(13)-a1004
['no miracles' argument]; blog sa(15)dec [is string theory science?].

@ __Critical assessments__: Larsson mp/01;
Faraggi ht/03-proc;
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 IJMPD(08)-a0805;
Zapata a0905 [results,
acceptance, and AdS/cft]; Schroer a0906;
comment pt(10)oct; Hedrich a1101 [epicycles!]; Giddings FP(13)-a1105; Rovelli FP(13)-a1108; Duff FP(11)-a1112-in, response Schroer a1201 [answering the critics]; Popławski a1210 [and matter with intrinsic spin]; 't Hooft FP(13); Dawid FP(13), 13 [r CP(14), FP(14)]; Copsey a1303 [orientifold instabilities]; Martins a1701 [Solomoff induction].

@ __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 JPCS(06)ht.

@ __Background independence__: Rahman ht/97, ht/97.

@ __Uniqueness (including p-branes)__: Bars & Pope GRG(89).

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**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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send feedback and suggestions to bombelli at olemiss.edu – modified 9
aug 2017