String theory: exact solutions, marginal deformations and hyperbolic spaces

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess‐Zumino‐Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off‐shell systems. Using a renormalization‐group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond‐Ramond field and in particular we analyze direct products of constant‐curvature spaces and find solutions with hyperbolic spaces.

[1]  M. Nakahara.  Geometry, Topology and Physics , 2018 .

[2]  K. Sfetsos,et al.  Renormalization‐group flows and charge transmutation in string theory , 2005, hep-th/0512086.

[3]  D. Orlando.  Coset models and D-branes in group manifolds , 2005, hep-th/0511210.

[4]  P. Spindel,et al.  Three-dimensional black holes from deformed anti de Sitter , 2005, hep-th/0504231.

[5]  D. Orlando.  ADS2 × S2 as an Exact Heterotic String Background , 2005, hep-th/0502213.

[6]  P. Petropoulos,et al.  Heterotic strings on homogeneous spaces , 2004, hep-th/0412220.

[7]  E. Silverstein,et al.  A new handle on de sitter compactifications , 2004, Journal of High Energy Physics.

[8]  P. Petropoulos,et al.  Electric/magnetic deformations of S3 and AdS3, and geometric cosets , 2004, hep-th/0405213.

[9]  H. Verlinde.  Superstrings on AdS_2 and Superconformal Matrix Quantum Mechanics , 2004, hep-th/0403024.

[10]  J. Rizos,et al.  Five-brane configurations, conformal field theories and the strong coupling problem , 2003, hep-th/0312300.

[11]  D. Israel.  Quantization of heterotic strings in a Goedel/Anti de Sitter spacetime and chronology protection , 2003, hep-th/0310158.

[12]  Ari Pakman,et al.  Type 0 strings in a 2-d black hole , 2003, Journal of High Energy Physics.

[13]  N. Drukker,et al.  Gödel's universe in a Supertube shroud. , 2003, Physical review letters.

[14]  D. Israel,et al.  Superstrings on NS5 backgrounds, deformed AdS3 and holography , 2003, hep-th/0306053.

[15]  D. Roggenkamp,et al.  Current-current deformations of conformal field theories, and WZW models , 2003, hep-th/0304234.

[16]  S. Yamaguchi,et al.  Supercoset CFT’s for String Theories on Non-compact Special Holonomy Manifolds , 2003, hep-th/0301164.

[17]  T. Quella,et al.  Asymmetric Cosets , 2002, hep-th/0212119.

[18]  M. Headrick,et al.  Spacetime Energy Decreases under World-sheet RG Flow , 2002, hep-th/0211063.

[19]  M. Rooman,et al.  Regular Poisson structures on massive non-rotating BTZ black holes , 2002, hep-th/0206189.

[20]  G. Gibbons,et al.  Uniqueness and nonuniqueness of static black holes in higher dimensions. , 2002, Physical review letters.

[21]  G. Gibbons,et al.  Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions , 2002, gr-qc/0203004.

[22]  G. Barnich,et al.  Covariant theory of asymptotic symmetries, conservation laws and central charges , 2001, hep-th/0111246.

[23]  E. Keski-Vakkuri,et al.  The Spectrum of Strings on BTZ Black Holes and Spectral Flow in the SL(2,R) WZW Model , 2001, hep-th/0110252.

[24]  T. Eguchi,et al.  CFT description of string theory compactified on non-compact manifolds with G2 holonomy , 2001, hep-th/0108091.

[25]  M. Atiyah,et al.  M-Theory Dynamics On A Manifold Of G_2 Holonomy , 2001, hep-th/0107177.

[26]  S. Gubser,et al.  Stability of AdS_p x M_q Compactifications Without Supersymmetry , 2001, hep-th/0105047.

[27]  A. Tseytlin,et al.  Conformal sigma models for a class of Tp,q spaces , 2000 .

[28]  J. Maldacena,et al.  Supergravity description of field theories on curved manifolds and a no go theorem , 2000, hep-th/0007018.

[29]  A. Giveon,et al.  Superstring theory on AdS3×G/H and boundary N = 3 superconformal symmetry , 2000, hep-th/0002104.

[30]  J. Maldacena,et al.  Strings in $AdS_{3}$ and SL(2,R) WZW Model, 1 , 2000 .

[31]  J. R. David.  String Theory and Black Holes , 1999, hep-th/9911003.

[32]  D. Kutasov,et al.  Little string theory in a double scaling limit , 1999, hep-th/9909110.

[33]  B. Zwiebach,et al.  Superstring theory on AdS2 × S2 as a coset supermanifold , 1999, hep-th/9907200.

[34]  D. Kutasov,et al.  Holography for Non-Critical Superstrings , 1999, hep-th/9907178.

[35]  K. Kondo,et al.  NON-ABELIAN STOKES THEOREM AND QUARK CONFINEMENT IN SU(3) YANG–MILLS GAUGE THEORY , 1999, hep-th/9906129.

[36]  K. Sfetsos.  Duality-invariant class of two-dimensional field theories , 1999, hep-th/9904188.

[37]  Sven Gnutzmann,et al.  Coherent states and the classical limit on irreducible representations , 1998 .

[38]  G. Gibbons,et al.  Black holes and Calogero models , 1998, hep-th/9812034.

[39]  R. Leigh,et al.  String theory in magnetic monopole backgrounds , 1998, hep-th/9812027.

[40]  O. Aharony,et al.  Linear dilatons, NS5-branes and holography , 1998, hep-th/9808149.

[41]  M. Duff,et al.  AdS3 × S3 (un) twisted and squashed, and an multiplet of dyonic strings , 1998, hep-th/9807173.

[42]  P. Forgács,et al.  On quantum T-duality in σ models , 1998, hep-th/9806068.

[43]  M. Heusler.  Stationary Black Holes: Uniqueness and Beyond , 1998, Living reviews in relativity.

[44]  R. Kallosh,et al.  Black holes and superconformal mechanics , 1998, hep-th/9804177.

[45]  M. Rooman,et al.  Gödel metric as a squashed anti-de Sitter geometry , 1998, gr-qc/9804027.

[46]  Kostas Skenderis,et al.  Brane intersections, anti-de Sitter space-times and dual superconformal theories , 1998, hep-th/9803231.

[47]  K. Stelle,et al.  BPS Branes in Supergravity , 1998, hep-th/9803116.

[48]  M. Duff,et al.  ADS5 S5 UNTWISTED , 1998, hep-th/9803061.

[49]  K. Sfetsos.  Poisson-Lie T-Duality beyond the classical level and the renormalization group , 1998, hep-th/9803019.

[50]  J. Teschner.  On structure constants and fusion rules in the SL(2,C)/SU(2)-WZNW model , 1997, hep-th/9712256.

[51]  J. Maldacena.  The Large-N Limit of Superconformal Field Theories and Supergravity , 1997, hep-th/9711200.

[52]  M. Byrd.  The geometry of SU(3) , 1997, physics/9708015.

[53]  Makoto Natsuume,et al.  STRING THEORY ON THREE-DIMENSIONAL BLACK HOLES , 1996, hep-th/9611041.

[54]  K. Stelle,et al.  Weyl group invariance and p-brane multiplets , 1996, hep-th/9602140.

[55]  P. Forgács,et al.  Perturbative Quantum (In)equivalence of Dual $\sigma$ Models in $2$ dimensions , 1996, hep-th/9601091.

[56]  C. Pope,et al.  p-brane solitons in maximal supergravities , 1995, hep-th/9512012.

[57]  Clifford V. Johnson,et al.  Heterotic coset models and (0,2) string vacua , 1995, hep-th/9509170.

[58]  E. Kiritsis,et al.  Infrared behavior of closed superstrings in strong magnetic and gravitational fields , 1995, hep-th/9508078.

[59]  Ferrara,et al.  N=2 extremal black holes. , 1995, Physical review. D, Particles and fields.

[60]  R. Khuri.  Black holes and solitons in string theory , 1995, hep-th/9506065.

[61]  A. Tseytlin.  Exact solutions of closed string theory , 1995, hep-th/9505052.

[62]  Clifford V. Johnson.  Heterotic Coset Models , 1994, hep-th/9409062.

[63]  G. Horowitz,et al.  New class of exact solutions in string theory. , 1994, Physical review. D, Particles and fields.

[64]  S. Forste.  A Truly marginal deformation of SL(2, R) in a null direction , 1994, hep-th/9407198.

[65]  M. Henneaux,et al.  Selfdual solutions of (2+1) Einstein gravity with a negative cosmological constant , 1994, hep-th/9407181.

[66]  Copeland,et al.  Low energy effective string cosmology. , 1994, Physical review. D, Particles and fields.

[67]  A. Tseytlin,et al.  Exact four dimensional string solutions and Toda-like sigma models from 'null-gauged' WZNW theories , 1994, hep-th/9402120.

[68]  C. Bachas,et al.  Exact string-theory instantons by dimensional reduction , 1993, hep-th/9311185.

[69]  Perry,et al.  String-dominated cosmology. , 1993, Physical review. D, Particles and fields.

[70]  Welch,et al.  String theory formulation of the three-dimensional black hole. , 1993, Physical review letters.

[71]  Gregory,et al.  Black strings and p-branes are unstable. , 1993, Physical review letters.

[72]  E. Kiritsis,et al.  Axial-Vector Duality as a Gauge Symmetry and Topology Change in String Theory , 1993, hep-th/9303016.

[73]  G. Horowitz,et al.  Exact Three Dimensional Black Holes in String Theory , 1993, hep-th/9302126.

[74]  A. Tseytlin.  Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories , 1993, hep-th/9302083.

[75]  Zanelli,et al.  Geometry of the 2+1 black hole. , 1993, Physical review. D, Particles and fields.

[76]  A. Tseytlin.  Effective action of the gauged WZW model and exact string solutions , 1993, hep-th/9301015.

[77]  Sayed Fawad Hassan,et al.  Marginal deformations of WZNW and coset models from O( d, d) transformations , 1992, hep-th/9210121.

[78]  K. Sfetsos.  Conformally exact results for SL(2, R) ⊗ SO(1, 1) d-2 / SO(1, 1) coset models , 1992, hep-th/9206048.

[79]  Zanelli,et al.  Black hole in three-dimensional spacetime. , 1992, Physical review letters.

[80]  A. Tseytlin.  Cosmological solutions with dilaton and maximally symmetric space in string theory , 1992, hep-th/9203033.

[81]  H. Verlinde,et al.  String Propagation in a Black Hole Geometry , 1992 .

[82]  M. Shifman,et al.  PERTURBATION THEORY IN THE WESS–ZUMINO–NOVIKOV–WITTEN MODEL , 1992 .

[83]  Gershon.  Exact solutions of four-dimensional black holes in string theory. , 1992, Physical review. D, Particles and fields.

[84]  A. Tseytlin.  Dilaton, winding modes and cosmological solutions , 1991, hep-th/9112004.

[85]  K. Gawȩdzki.  Non-compact WZW conformal field theories , 1991, hep-th/9110076.

[86]  Petr Hořava.  Some exact solutions of string theory in four and five dimensions , 1991, hep-th/9110067.

[87]  Horne,et al.  An equivalence between momentum and charge in string theory. , 1991, Physical review letters.

[88]  J. Horne,et al.  Exact black string solutions in three dimensions , 1991, hep-th/9108001.

[89]  Witten,et al.  String theory and black holes. , 1991, Physical review. D, Particles and fields.

[90]  C. Callan,et al.  Worldsheet approach to heterotic instantons and solitons , 1991 .

[91]  M. Porrati,et al.  On N=4 extended super-Liouville theory , 1991 .

[92]  H. Osborn.  General bosonic σ models and string effective actions , 1990 .

[93]  P. Petropoulos.  Comments on SU(1,1) string theory , 1990 .

[94]  C. Bachas,et al.  Gauged supergravity vacua in string theory , 1990 .

[95]  J. Ellis,et al.  An expanding universe in string theory , 1989 .

[96]  Y. Kazama,et al.  New N=2 Superconformal Field Theories and Superstring Compactification , 1989 .

[97]  S. Chaudhuri,et al.  A criterion for integrably marginal operators , 1989 .

[98]  Y. Kazama,et al.  Characterization of N=2 superconformal models generated by the coset space method , 1989 .

[99]  D. Gepner.  Space-time supersymmetry in compactified string theory and superconformal models , 1988 .

[100]  Sung-Kil Yang,et al.  Modular invariance in N=2 superconformal field theories , 1987 .

[101]  C. Hull.  The two-loop -function for s-models with torsion , 1987 .

[102]  T. H. Buscher,et al.  A symmetry of the string background field equations , 1987 .

[103]  Y. Matsuo.  Character Formula of C≪1 Unitary Representation of N=2 Superconformal Algebra , 1987 .

[104]  V. Dobrev.  Characters of the Unitarizable Highest Weight Modules over the N=2 Superconformal Algebras , 1987, 0708.1719.

[105]  A. Perelomov.  Chiral models: Geometrical aspects , 1987 .

[106]  C. Callan,et al.  Strings in background fields , 1985 .

[107]  E. Braaten,et al.  Torsion and geometrostasis in nonlinear sigma models , 1985 .

[108]  D. Friedan,et al.  Nonlinear models in 2 + ε dimensions☆ , 1985 .

[109]  Christopher M. Hull,et al.  Twisted multiplets and new supersymmetric non-linear σ-models☆☆☆★ , 1984 .

[110]  V. G. Knizhnik,et al.  Current Algebra and Wess-Zumino Model in Two-Dimensions , 1984 .

[111]  E. Witten.  Non-abelian bosonization in two dimensions , 1984 .

[112]  A. Polyakov,et al.  Theory of nonabelian goldstone bosons in two dimensions , 1983 .

[113]  J. Tiomno,et al.  Homogeneity of Riemannian space-times of Gödel type , 1983 .

[114]  D. Freedman,et al.  The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model , 1981 .

[115]  D. Friedan,et al.  NONLINEAR MODELS IN 2 +<-DIMENSIONS , 1980 .

[116]  Werner Israel,et al.  Event Horizons in Static Vacuum Space-Times , 1967 .

[117]  A. Borel,et al.  CHARACTERISTIC CLASSES AND HOMOGENEOUS SPACES, I.* , 1958 .

[118]  P. Petropoulos,et al.  Superstrings on NS 5 backgrounds , deformed AdS 3 and holography ∗ , 2008 .

[119]  J. Boer,et al.  String theory : from gauge interactions to cosmology , 2006 .

[120]  M Rooman,et al.  Gödel metric as a squashed anti-de Sitter geometry , 1998 .

[121]  N. Vilenkin,et al.  Representation of Lie groups and special functions , 1991 .

[122]  K. Gawȩdzki.  Noncompact WZW conformal field theories , 1991 .

[123]  E. Kiritsis.  CHARACTER FORMULAE AND THE STRUCTURE OF THE REPRESENTATIONS OF THE N=1, N=2 SUPERCONFORMAL ALGEBRAS , 1988 .

[124]  F. Müller-Hoissen,et al.  Coset spaces and ten-dimensional unified theories , 1988 .

[125]  Zongan Qiu,et al.  Modular invariant partition functions for parafermionic field theories , 1987 .

[126]  D. Gepner.  New conformal field theories associated with lie algebras and their partition functions , 1987 .

[127]  B. Sakita.  FIELD THEORY OF CURRENTS. , 1969 .

[128]  C. Sommerfield.  CURRENTS AS DYNAMICAL VARIABLES. , 1968 .