×

A philosopher looks at string dualities. (English) Zbl 1228.81043

Summary: Many of the advances in string theory have been generated by the discovery of new duality symmetries connecting what were once thought to be distinct theories. Indeed, duality has played an enormously important role in the creation and development of numerous theories in physics and numerous fields of mathematics. Dualities often lie at those fruitful intersections at which mathematics and physics are especially strongly intertwined. In this paper I describe several of these dualities and unpack some of their philosophical implications, focusing primarily on string theoretic dualities.

MSC:

81P05 General and philosophical questions in quantum theory
81T99 Quantum field theory; related classical field theories
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aspinwall, P. S., Some relationships between dualities in string theory, Nuclear Physics B (Proceedings Supplements), 46, 30-38 (1996) · Zbl 0957.81599
[2] Bagger, J., Strings and Riemann surfaces, (Slansky, R.; West, G., The Santa Fe TASI-87, vol. 2 (1988), World Scientific), 688-729
[3] Ballman, W., Lectures on Kähler manifolds, ESI lectures in mathematics and physics (2006), American Mathematical Society
[4] Belot, G., Symmetry and gauge freedom, Studies in History and Philosophy of Modern Physics, 34, 2, 189-225 (2002) · Zbl 1222.81210
[5] Brading, K., & Castellani, E. (Eds.). (2003). Symmetries in physics: Philosophical reflections; Brading, K., & Castellani, E. (Eds.). (2003). Symmetries in physics: Philosophical reflections · Zbl 1206.00016
[6] Candelas, P.; Horowitz, G.; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nuclear Physics B, 258, 46-74 (1985)
[7] Candelas, P.; Horowitz, G.; Strominger, A.; Witten, E.; de la Ossa, X. C.; Green, P. S., A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Physics Letters B, 258, 118-126 (1991)
[8] Castellani, E., Dualities and intertheoretic relations, (Suárez, M.; Dorato, M.; Rédei, M., EPSA philosophical issues in the sciences: Launch of the European philosophy of science association (2009), Springer), 9-19
[9] Castellani, E., Reductionism, emergence, and effective field theories, Studies in History and Philosophy of Modern Physics, 33, 2, 251-267 (2002) · Zbl 1222.81010
[10] Cox, D. A.; Katz, S., Mirror symmetry and algebraic geometry (1999), American Mathematical Society · Zbl 0951.14026
[11] Dawid, R. (2007). Scientific realism in the age of string theory. Physics and Philosophy; Dawid, R. (2007). Scientific realism in the age of string theory. Physics and Philosophy
[12] Dawid, R., Underdetermination and theory succession from the perspective of string theory, Philosophy of Science, 73, 298-322 (2006)
[13] Dirac, P. A.M., The theory of magnetic poles, Physical Review, 74, 817-830 (1948) · Zbl 0034.27604
[14] D’Hoker, E.; Phong, D. H., The geometry of string perturbation theory, Reviews of Modern Physics, 60, 917-1065 (1988)
[15] Dolan, R.; Horn, D.; Schmid, C., Prediction of regge parameters of \(\rho\) poles from low-energy \(\pi N\) data, Physical Review Letters, 19, 402-407 (1967)
[16] Earman, J., Underdetermination, realism and reason, Midwest Studies in Philosophy, XVIII, 19-38 (1993)
[17] Fuchs, J.; Schweigert, C., Symmetries, lie algebras and representations: A graduate course for physicists (1997), Cambridge University Press · Zbl 0923.17001
[18] Galison, P., Mirror symmetry: Persons, values, and objects, (Norton Wise, M.; etal., Growing explanations: Historical perspectives on recent science (1999), Duke University Press), 23-61
[19] Gasperini, M., & Maharana, J. (Eds.) (2008). String theory and fundamental interactions. Gabriele Veneziano and theoretical physics: Historical and contemporary perspectives; Gasperini, M., & Maharana, J. (Eds.) (2008). String theory and fundamental interactions. Gabriele Veneziano and theoretical physics: Historical and contemporary perspectives · Zbl 1138.81005
[20] Giddings, S. B.; Kachru, S.; Polchinski, J., Hierarchies from fluxes in string compactifications, Physical Review D, 66, 106006-106012 (2001)
[21] Giveon, A.; Porrati, M.; Rabinovici, E., Target space duality in string theory, Physics Reports, 244, 2-3, 77-202 (1994)
[22] Glymour, C., Indistinguishable space-times and the fundamental group, (Earman, J.; Glymour, C.; Stachel, J., Foundations of spacetime theories. Minnesota studies in the philosophy of science, vol. VII (1977), University of Minnesota Press: University of Minnesota Press Minneapolis), 50-60
[23] Greene, B., Aspects of quantum geometry, (Phong, D. H.; Vinet, L.; Yau, S.-T., Mirror symmetry III (1999), American Mathematical Society), 1-67 · Zbl 0923.32023
[24] Gross, D., Renormalization groups, (Deligne, P.; etal., Quantum fields and strings: Course for mathematicians, vol. 1 (1999), American Mathematical Society), 551-593 · Zbl 1170.81417
[25] Gross, D., Where do we stand in fundamental (string) theory?, Physica Scripta, T117, 102-105 (2005)
[26] Hartmann, S., Effective field theories, reductionism and scientific explanation, Studies in History and Philosophy of Modern Physics, 32, 2, 267-304 (2001) · Zbl 1222.00029
[27] Harvey, J. A.; Strominger, A., The heterotic string is a soliton, Nuclear Physics B, 449, 3, 535-552 (1995) · Zbl 1076.81555
[28] Healey, R., Gauging what’s real: The conceptual foundations of contemporary gauge theories (2007), Oxford University Press · Zbl 1158.81003
[29] Hori, K.; Katz, S.; Klemm, A.; Vafa, C.; Vakil, R.; Zaslow, E., Mirror symmetry (2003), American Mathematical Society · Zbl 1044.14018
[30] Huggett, N., Renormalization and the disunity of science, (Kuhlmann, M.; Lyre, H.; Wayne, A., Ontological aspects of quantum field theory (2002), World Scientific: World Scientific New Jersey), 255-277
[31] Huggett, N.; Weingard, R., The renormalization group and effective field theories, Synthese, 102, 171-194 (1995) · Zbl 1058.81604
[32] Ismael, J.; van Fraassen, B., Symmetry as a guide to superfluous theoretical structure, (Brading, K.; Castellani, E., Symmetries in physics: Philosophical reflections (2003), Cambridge University Press)
[33] Jacob, M. (Ed.). (1974). Dual theory. Physics reports reprints book series; Jacob, M. (Ed.). (1974). Dual theory. Physics reports reprints book series
[34] Lian, B. H.; Liu, K.; Yau, S.-T., The Candelas-de la Ossa-Green-Parkes formula, Nuclear Physics B (Proceedings Supplements), 67, 1-3, 106-114 (2000) · Zbl 0988.81104
[35] Lyre, H., Does the Higgs mechanism exist?, International Studies in the Philosophy of Science, 22, 2, 119-133 (2008) · Zbl 1158.81302
[36] Magnus, P. D., Reckoning the shape of everything: Underdetermination and cosmotopology, British Journal for the Philosophy of Science, 56, 3, 541-557 (2005) · Zbl 1086.83512
[37] Maldacena, J., The large N limit of superconformal field theories and supergravity, Advances in Theoretical and Mathematical Physics, 2, 231-252 (1998) · Zbl 0914.53047
[38] Malament, D., Observationally indistinguishable spacetimes, (Earman, J.; Glymour, C.; Stachel, J., Foundations of spacetime theories. Minnesota studies in the philosophy of science, vol. VII (1977), University of Minnesota Press: University of Minnesota Press Minneapolis), 61-80
[39] Morrow, J.; Kodaira, K., Complex manifolds (1971), American Mathematical Society · Zbl 0325.32001
[40] Myers, R. C.; Vázquez, S. E., Quark soup Al Dente: Applied superstring theory, Classical and Quantum Gravity, 25, 11, 114008-114021 (2008) · Zbl 1144.83333
[41] Norton, J. D., Must theory underdetermine evidence?, (Carrier, M.; Howard, D.; Kourany, J., The challenge of the social and the pressure of practice: Science and values revisited (2008), University of Pittsburgh Press: University of Pittsburgh Press Pittsburgh), 17-44
[42] Olive, D. I., Introduction to duality, (Olive, D. I.; West, P. C., Duality and supersymmetric theories (1999), Cambridge University Press), 62-94 · Zbl 0957.81062
[43] Polchinski, J., Recent results in string duality, Progress of Theoretical Physics (Supplement), 123, 9-18 (1996)
[44] Polyakov, A. M., Quantum geometry of bosonic strings, Physics Letters B, 103, 3, 207-210 (1981)
[45] Polyakov, A. M., Quantum geometry of fermionic strings, Physics Letters B, 103, 3, 211-213 (1981)
[46] Rickles, D. (2010). Mirror symmetry and other miracles in superstring theory. Foundations of Physics\( \langle\) http://dx.doi.org/10.1007/s \(10701-010-9504-5 \rangle \); Rickles, D. (2010). Mirror symmetry and other miracles in superstring theory. Foundations of Physics\( \langle\) http://dx.doi.org/10.1007/s \(10701-010-9504-5 \rangle \)
[47] Rubinstein, H., The birth of the Veneziano model and string theory, (Gasperini, M.; Maharana, J., String theory and fundamental interactions. Gabriele Veneziano and theoretical physics: Historical and contemporary perspectives (2008), Springer), 47-58 · Zbl 05353473
[48] Schlichenmaier, M., An introduction to Riemann surfaces, algebraic curves and moduli spaces (2009), Springer
[49] Seiberg, N., Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nuclear Physics B, 435, 129-146 (1995) · Zbl 1020.81912
[50] Sen, A., String-string duality conjecture in six dimensions and charged solitonic strings, Nuclear Physics B, 450, 1-2, 103-114 (1995) · Zbl 0982.81520
[51] Smeenk, C., The elusive Higgs mechanism, Philosophy of Science, 73, 487-499 (2006)
[52] Taylor, C. C., String theory, quantum gravity, and locality, (Fine, A.; Leplin, J., Proceedings of the philosophy of science association 1988, vol. 2 (1988), Philosophy of Science Association), 107-111 · Zbl 0676.53096
[53] Thurston, W. P., Three-dimensional geometry and topology (1997), Princeton University Press
[54] Tignol, J.-P., Galois’ theory of algebraic equations (2001), World Scientific
[55] Vafa, C., Lectures on strings and dualities, (Gava, E.; etal., 1996 summer school in high energy physics and cosmology (1996), World Scientific), 66-117
[56] Vafa, C. (1998). Geometric physics. In G. Fischer, & U. Rehmann, (Eds.), Proceedings of the international congress of mathematics; Vafa, C. (1998). Geometric physics. In G. Fischer, & U. Rehmann, (Eds.), Proceedings of the international congress of mathematics · Zbl 0907.53043
[57] Veneziano, G., Construction of a crossing-symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cimento A, 57, 190-197 (1968)
[58] Weingard, R., A philosopher looks at string theory, (Fine, A.; Leplin, J., Proceedings of the philosophy of science association 1988, vol. 2 (1988), Philosophy of Science Association), 95-106, (Reprinted in Physics meets philosophy at the Planck scale, Callender, C., & Huggett, N. (Eds.) (pp. 138-151)
[59] Wigner, E., Symmetry and conservation laws, (Wigner, E., Symmetries and reflections: Scientific essays (1964), University of Indiana Press), 14-27, (Reprinted, 1967)
[60] Witten, E., String theory dynamics in various dimensions, Nuclear Physics B, 443, 1-2, 85-126 (1995) · Zbl 0990.81663
[61] Witten, E., Reflections on the fate of spacetime, Physics Today, 24-30 (1996)
[62] Witten, E., Duality, spacetime and quantum mechanics, Physics Today, May, 28-33 (1997)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.