# zbMATH — the first resource for mathematics

Dualities of fields and strings. (English) Zbl 1371.81213
Summary: Duality, the equivalence between seemingly distinct quantum systems, is a curious property that has been known for at least three quarters of a century. In the past two decades it has played a central role in mapping out the structure of theoretical physics. I discuss the unexpected connections that have been revealed among quantum field theories and string theories. Written for a special issue of Studies in History and Philosophy of Modern Physics.

##### MSC:
 81T10 Model quantum field theories 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 00A79 Physics
##### Keywords:
quantum field theory; string theory; duality
Full Text:
##### References:
 [1] Alishahiha, M., Karch, A., Silverstein, E., & Tong, D. (2005). The dS/dS correspondence. AIP Conference Proceedings 743, 393 [hep-th/0407125]. [2] Almheiri, A.; Marolf, D.; Polchinski, J.; Sully, J., Journal of High Energy Physics, 1302, 062, (2013), arXiv:1207.3123 [hep-th] [3] Argyres, P. C.; Douglas, M. R., New phenomena in SU(3) supersymmetric gauge theory, Nuclear Physics B, 448, 93, (1995), [hep-th/9505062] · Zbl 1009.81572 [4] Banks, T.; Dixon, L. J., Constraints on string vacua with space-time supersymmetry, Nuclear Physics B, 307, 93, (1988) [5] Banks, T.; Susskind, L.; Peskin, M. E., Difficulties for the evolution of pure states into mixed states, Nuclear Physics B, 244, 125, (1984) [6] Banks, T.; Fischler, W.; Shenker, S. H.; Susskind, L., M theory as a matrix modela conjecture, Physical Review D, 55, 5112, (1997), [hep-th/9610043] [7] Bekenstein, J. D., Black holes and entropy, Physical Review D, 7, 2333, (1973) · Zbl 1369.83037 [8] Brandt, R. A.; Neri, F.; Zwanziger, D., Lorentz invariance from classical particle paths in quantum field theory of electric and magnetic charge, Physical Review D, 19, 1153, (1979) [9] Callan, C. G.; Harvey, J. A.; Strominger, A., World sheet approach to heterotic instantons and solitons, Nuclear Physics B, 359, 611, (1991) [10] Cardy, J. L., Duality and the theta parameter in abelian lattice models, Nuclear Physics B, 205, 17, (1982) [11] Cardy, J. L.; Rabinovici, E., Phase structure of Z(p) models in the presence of a theta parameter, Nuclear Physics B, 205, 1, (1982) [12] Coleman, S. R., The quantum sine-Gordon equation as the massive Thirring model, Physical Review D, 11, 2088, (1975) [13] Coleman, S. R.; Mandula, J., All possible symmetries of the S matrix, Physical Review, 159, 1251, (1967) · Zbl 0168.23702 [14] Cremmer, E.; Julia, B.; Scherk, J., Supergravity theory in eleven-dimensions, Physics Letters B, 76, 409, (1978) [15] Dai, J.; Leigh, R. G.; Polchinski, J., New connections between string theories, Modern Physics Letters A, 4, 2073, (1989) [16] de Wit, B.; Hoppe, J.; Nicolai, H., On the quantum mechanics of supermembranes, Nuclear Physics B, 305, 545, (1988) [17] Dine, M.; Huet, P. Y.; Seiberg, N., Large and small radius in string theory, Nuclear Physics B, 322, 301, (1989) [18] Dirac, P. A.M., Quantized singularities in the electromagnetic field, Proceedings of the Royal Society of London A, 133, 60, (1931) · Zbl 0002.30502 [19] Duff, M. J., Strong/weak coupling duality from the dual string, Nuclear Physics B, 442, 47, (1995), [hep-th/9501030] · Zbl 0990.81661 [20] Duff, M. J.; Howe, P. S.; Inami, T.; Stelle, K. S., Superstrings in $$D = 10$$ from supermembranes in $$D = 11$$, Physics Letters B, 191, 70, (1987) [21] Dyson, F. J., Divergence of perturbation theory in quantum electrodynamics, Physical Review, 85, 631, (1952) · Zbl 0046.21501 [22] Font, A.; Ibanez, L. E.; Lust, D.; Quevedo, F., Strong-weak coupling duality and nonperturbative effects in string theory, Physics Letters B, 249, 35, (1990) [23] Gaiotto, D., $$N = 2$$ dualities, Journal of High Energy Physics, 1208, 034, (2012), [arXiv:0904.2715 [hep-th]] [24] Gary, M., & Giddings, S.B. (2011). Constraints on a fine-grained AdS/CFT correspondence, arXiv:1106.3553 [hep-th]. [25] Giveon, A.; Porrati, M.; Rabinovici, E., Target space duality in string theory, Physics Report, 244, 77, (1994), [hep-th/9401139] [26] Goddard, P.; Nuyts, J.; Olive, D. I., Gauge theories and magnetic charge, Nuclear Physics B, 125, 1, (1977) [27] Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M., Gauge theory correlators from non-critical string theory, Physics Letters B, 428, 105, (1998), arXiv:hep-th/9802109 · Zbl 1355.81126 [28] Hanada, M.; Hyakutake, Y.; Ishiki, G.; Nishimura, J., Holographic description of quantum black hole on a computer, Science, 344, 882, (2014), arXiv:1311.5607 [hep-th] [29] Hartnoll, S. A., Lectures on holographic methods for condensed matter physics, Classical and Quantum Gravity, 26, 224002, (2009), arXiv:0903.3246 [hep-th] · Zbl 1181.83003 [30] Hawking, S. W., Particle creation by black holes, Communications in Mathematical Physics, 43, 199, (1975), [Erratum-Communications in Mathematical Physics 46, 206 (1976)] · Zbl 1378.83040 [31] Hawking, S. W., Breakdown of predictability in gravitational collapse, Physical Review D, 14, 2460, (1976) [32] Heemskerk, I.; Penedones, J.; Polchinski, J.; Sully, J., Holography from conformal field theory, Journal of High Energy Physics, 0910, 079, (2009), arXiv:0907.0151 [hep-th] [33] ׳t Hooft, G., A planar diagram theory for strong interactions, Nuclear Physics B, 72, 461, (1974) [34] ׳t Hooft, G., Magnetic monopoles in unified gauge theories, Nuclear Physics B, 79, 276, (1974) [35] ׳t Hooft, G., On the phase transition towards permanent quark confinement, Nuclear Physics B, 138, 1, (1978) [36] ׳t Hooft, G. (1993). Dimensional reduction in quantum gravity, arXiv:gr-qc/9310026. [37] Horava, P., Background duality of open string models, Physics Letters B, 231, 251, (1989) [38] Horava, P.; Witten, E., Heterotic and type I string dynamics from eleven-dimensions, Nuclear Physics B, 460, 506, (1996), [hep-th/9510209] · Zbl 1004.81525 [39] Hori, K., Katz, S., Klemm, A., Pandharipande, R., Thomas, R., Vafa, C., et al. (2003). Mirror symmetry. In Clay mathematics monographs (Vol. 1). Providence, RI: American Mathematical Society. · Zbl 1044.14018 [40] Horowitz, G. T.; Strominger, A., Black strings and P-branes, Nuclear Physics B, 360, 197, (1991) [41] Hull, C. M.; Townsend, P. K., Unity of superstring dualities, Nuclear Physics B, 438, 109, (1995), [hep-th/9410167] · Zbl 1052.83532 [42] Isgur, N.; Wise, M. B., Weak decays of heavy mesons in the static quark approximation, Physics Letters B, 232, 113, (1989) [43] Ishibashi, N.; Kawai, H.; Kitazawa, Y.; Tsuchiya, A., A large N reduced model as superstring, Nuclear Physics B, 498, 467, (1997), [hep-th/9612115] · Zbl 0979.81567 [44] Itzhaki, N.; Maldacena, J. M.; Sonnenschein, J.; Yankielowicz, S., Supergravity and the large N limit of theories with sixteen supercharges, Physical Review D, 58, 046004, (1998), [hep-th/9802042] [45] Kikkawa, K.; Yamasaki, M., Casimir effects in superstring theories, Physics Letters B, 149, 357, (1984) [46] Kovtun, P.; Son, D. T.; Starinets, A. O., Viscosity in strongly interacting quantum field theories from black hole physics, Physical Review Letter, 94, 111601, (2005), [hep-th/0405231] [47] Kramers, H. A.; Wannier, G. H., Statistics of the two-dimensional ferromagnet. part 1, Physical Review, 60, 252, (1941) · Zbl 0027.28505 [48] Maldacena, J. M., The large N limit of superconformal field theories and supergravity, Advances in Theoretical and Mathematical Physics, 2, 231, (1998), [International Journal of Theoretical Physics 38, 1113 (1999)] arXiv:hep-th/9711200 · Zbl 0914.53047 [49] Mandelstam, S., Charge-monopole duality and the phases of nonabelian gauge theories, Physical Review D, 19, 2391, (1979) [50] Montonen, C.; Olive, D. I., Magnetic monopoles as gauge particles?, Physics Letters B, 72, 117, (1977) [51] Nair, V. P.; Shapere, A. D.; Strominger, A.; Wilczek, F., Compactification of the twisted heterotic string, Nuclear Physics B, 287, 402, (1987) [52] Narain, K. S., New heterotic string theories in uncompactified dimensions 10, Physics Letters B, 169, 41, (1986) [53] Nishioka, T.; Ryu, S.; Takayanagi, T., Holographic entanglement entropy: an overview, Journal of Physics A, 42, 504008, (2009), arXiv:0905.0932 [hep-th] · Zbl 1179.81138 [54] Onsager, L., Crystal statistics. 1. A two-dimensional model with an order disorder transition, Physical Review, 65, 117, (1944) · Zbl 0060.46001 [55] Osborn, H., Topological charges for N=4 supersymmetric gauge theories and monopoles of spin 1, Physics Letters B, 83, 321, (1979) [56] Polchinski, J., Dirichlet branes and Ramond-Ramond charges, Physical Review Letter, 75, 4724, (1995), [hep-th/9510017] · Zbl 1020.81797 [57] Polchinski, J.; Witten, E., Evidence for heterotic—type I string duality, Nuclear Physics B, 460, 525, (1996), [hep-th/9510169] · Zbl 1004.81526 [58] Polyakov, A. M., Particle spectrum in the quantum field theory, JETP Letter, 20, 194, (1974), [Pisma Zh. Eksp. Teor. Fiz. 20, 430 (1974)] [59] Polyakov, A. M., Gauge fields and strings, Contemporary Concepts in Physics, 3, 1, (1987) [60] Quevedo, F., Duality and global symmetries, Nuclear Physics B—Proceedings Supplements, 23, Suppl. 61A, (1998), [hep-th/9706210] · Zbl 0985.81672 [61] Sakai, N.; Senda, I., Vacuum energies of string compactified on torus, Progress of Theoretical Physics, 75, 692, (1986), [Erratum-Progress of Theoretical Physics 77, 773 (1987)] [62] Savit, R., Duality in field theory and statistical systems, Review of Modern Physics, 52, 453, (1980) [63] Seiberg, N., Exact results on the space of vacua of four-dimensional SUSY gauge theories, Physical Review D, 49, 6857, (1994), [hep-th/9402044] [64] Seiberg, N. (2015). Breakthrough prize symposium in physics, Stanford, 〈https://www.youtube.com/watch?v=Hi3e0HVxlFo&list=PLyF3OMOiy3nEO1yE2Gw-h4U0GQD06HlsZ&index=6〉. [65] Seiberg, N.; Witten, E., Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nuclear Physics B, 426, 19, (1994), [Erratum-Nuclear Physics B 430, 485 (1994)] [hep-th/9407087] · Zbl 0996.81510 [66] Sen, A., Dyon-monopole bound states, selfdual harmonic forms on the multi-monopole moduli space, and SL(2,Z) invariance in string theory, Physics Letters B, 329, 217, (1994), [hep-th/9402032] · Zbl 1190.81113 [67] Senthil, T.; Vishwanath, A.; Balents, L.; Sachdev, S.; Fisher, M. P.A., Deconfined quantum critical points, Science, 303, 1490, (2004) [68] Shahar, D.; Tsui, D. C.; Shayegan, M.; Shimshoni, E.; Sondhi, S. L., Evidence for charge-flux duality near the quantum Hall liquid to insulator transition, Science, 274, 589, (1996) [69] Stanley, H. E., Spherical model as the limit of infinite spin dimensionality, Physical Review, 176, 718, (1968) [70] Strominger, A., The ds/CFT correspondence, Journal of High Energy Physics, 0110, 034, (2001), [hep-th/0106113] [71] Strominger, A.; Vafa, C., Microscopic origin of the bekenstein-Hawking entropy, Physics Letters B, 379, 99, (1996), [hep-th/9601029] · Zbl 1376.83026 [72] Susskind, L., The world as a hologram, Journal of Mathematical Physics, 36, 6377, (1995), arXiv:hep-th/9409089 · Zbl 0850.00013 [73] Susskind, L. (1995b). After-dinner talk at Strings. University of Southern California. [74] Susskind, L. (1997). Another conjecture about m(atrix) theory [hep-th/9704080]. [75] Townsend, P. K., The eleven-dimensional supermembrane revisited, Physics Letters B, 350, 184, (1995), [hep-th/9501068] [76] Vafa, C.; Witten, E., A strong coupling test of S duality, Nuclear Physics B, 431, 3, (1994), [hep-th/9408074] · Zbl 0964.81522 [77] Weinberg, S., Anthropic bound on the cosmological constant, Physical Review Letter, 59, 2607, (1987) [78] Weinberg, S.; Witten, E., Limits on massless particles, Physics Letters B, 96, 59, (1980) [79] Wilson, K. G., Quantum field theory models in less than four-dimensions, Physical Review D, 7, 2911, (1973) [80] Wilson, K. G., The renormalization group and critical phenomena, Reviews of Modern Physics, 55, 583, (1983) [81] Witten, E. (1995a). Some comments on string dynamics. In Los Angeles 1995, Future perspectives in string theory (pp. 501-523) [hep-th/9507121]. [82] Witten, E., String theory dynamics in various dimensions, Nuclear Physics B, 443, 85, (1995), [hep-th/9503124] · Zbl 0990.81663 [83] Witten, E., Bound states of strings and p-branes, Nuclear Physics B, 460, 335, (1996), [hep-th/9510135] · Zbl 1003.81527 [84] Witten, E., Magic, mystery, and matrix, Notices of the American Mathematical Society, 45, 1124, (1998) · Zbl 0907.53049 [85] Witten, E., Anti-de Sitter space and holography, Advances in Theoretical and Mathematical Physics, 2, 253, (1998), arXiv:hep-th/9802150 · Zbl 0914.53048 [86] Witten, E., Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Advances in Theoretical and Mathematical Physics, 2, 505, (1998), [hep-th/9803131] · Zbl 1057.81550 [87] Witten, E. (2001). Quantum gravity in de Sitter space [hep-th/0106109]. [88] Witten, E.; Olive, D. I., Supersymmetry algebras that include topological charges, Physics Letters B, 78, 97, (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.