# zbMATH — the first resource for mathematics

N=2 supersymmetric RG flows and the IIB dilaton. (English) Zbl 0971.83513
Summary: We show that there is a non-trivial relationship between the dilaton of IIB supergravity, and the coset of scalar fields in five-dimensional, gauged N=8 supergravity. This has important consequences for the running of the gauge coupling in massive perturbations of the AdS/CFT correspondence. We conjecture an exact analytic expression for the ten-dimensional dilaton in terms of five-dimensional quantities, and we test this conjecture. Specifically, we construct a family of solutions to IIB supergravity that preserve half of the supersymmetries, and are lifts of supersymmetric flows in five-dimensional, gauged N=8 supergravity. Via the AdS/CFT correspondence these flows correspond to softly broken N=4, large N Yang-Mills theory on part of the Coulomb branch of N=2 supersymmetric Yang-Mills. Our solutions involve non-trivial backgrounds for all the tensor gauge fields as well as for the dilaton and axion.

##### MSC:
 83E50 Supergravity 81T60 Supersymmetric field theories in quantum mechanics 81T17 Renormalization group methods applied to problems in quantum field theory
Full Text:
##### References:
 [1] Maldacena, J., The large $$N$$ limit of superconformal field theories and supergravity, Adv. theor. math. phys., 2, 231, (1998) · Zbl 0914.53047 [2] Gubser, S.S.; Klebanov, I.R.; Polyakov, A.M., Gauge theory correlators from non-critical string theory, Phys. lett. B, 428, 105, (1998) · Zbl 1355.81126 [3] Witten, E., Anti-de-Sitter space and holography, Adv. theor. math. phys., 2, 253, (1998) · Zbl 0914.53048 [4] Günaydin, M.; Romans, L.J.; Warner, N.P.; Günaydin, M.; Romans, L.J.; Warner, N.P., Compact and non-compact gauged supergravity theories in five dimensions, Phys. lett. B, Nucl. phys. B, 272, 598, (1986) [5] Pernici, M.; Pilch, K.; van Nieuwenhuizen, P., Gauged $$N=8$$, $$D=5$$ supergravity, Nucl. phys. B, 259, 460, (1985) [6] Distler, J.; Zamora, F.; Distler, J.; Zamora, F., Chiral symmetry breaking in the AdS/CFT correspondence, Adv. theor. math. phys., Jhep, 5, 005, (2000) · Zbl 0990.81726 [7] Girardello, L.; Petrini, M.; Porrati, M.; Zaffaroni, A., Novel local CFT and exact results on perturbations of $$N=4$$ super yang – mills from AdS dynamics, Jhep, 12, 022, (1998) [8] Khavaev, A.; Pilch, K.; Warner, N.P., New vacua of gauged $$N=8$$ supergravity in five dimensions, Phys. lett. B, 487, 14, (2000) · Zbl 1050.81686 [9] Pilch, K.; Warner, N.P., A new supersymmetric compactification of chiral IIB supergravity, Phys. lett. B, 487, 22, (2000) · Zbl 1050.81689 [10] Balasubramanian, V.; Kraus, P.; Lawrence, A., Bulk vs. boundary dynamics in anti-de-Sitter space – time, Phys. rev. D, 59, 046003, (1999) [11] Freedman, D.Z.; Gubser, S.S.; Pilch, K.; Warner, N.P., Continuous distribution of D3-branes and gauged supergravity, Jhep, 07, 038, (2000) · Zbl 1052.83529 [12] Novikov, V.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V., Exact Gell-Mann-low function of supersymmetric yang – mills theories from instanton calculus, Nucl. phys. B, 229, 381, (1983) [13] Freedman, D.Z.; Gubser, S.S.; Pilch, K.; Warner, N.P., Renormalization group flows from holography — supersymmetry and a c-theorem, CERN-TH-99-86 · Zbl 0976.83067 [14] Gubser, S., Curvature singularities: the good, the bad, and the naked, PUPT-1916 · Zbl 0984.83036 [15] Schwarz, J.H., Covariant field equations of chiral $$N=2$$, $$D=10$$ supergravity, Nucl. phys. B, 226, 269, (1983) [16] Howe, P.; West, P., The complete $$N=2$$$$D=10$$ supergravity, Nucl. phys. B, 238, 181, (1984) [17] Castellani, L.; Pesando, I., The complete superspace action of chiral $$D=10$$, $$N=2$$ supergravity, Int. J. mod. phys. A, 8, 1125, (1993) [18] Cvetič, M.; Lü, H.; Pope, C.N., Geometry of the embedding of scalar manifolds in $$D=11$$ and $$D=10$$, Nucl. phys. B, 584, 149, (2000) · Zbl 0985.83032 [19] Petrini, M.; Zaffaroni, A., The holographic RG flow to conformal and non-conformal theory [20] Johnson, C.V.; Peet, A.W.; Polchinski, J., Gauge theory and the excision of repulson singularities, Phys. rev. D, 61, 086001, (2000) [21] Argyres, P.C.; Douglas, M.R., New phenomena in $$SU(3)$$ supersymmetric gauge theory, Nucl. phys. B, 448, 93, (1995) · Zbl 1009.81572 [22] Argyres, P.C.; Ronen Plesser, M.; Seiberg, N.; Witten, E., New $$N=2$$ superconformal field theories in four dimensions, Nucl. phys. B, 461, 71, (1996) · Zbl 1004.81557 [23] Girardello, L.; Petrini, M.; Porrati, M.; Zaffaroni, A., The supergravity dual of $$N=1$$ super yang – mills theory, Nucl. phys. B, 569, 451, (2000) · Zbl 0951.81056 [24] Behrndt, K., Domain walls of $$D=5$$ supergravity and fixpoints of $$N=1$$ super yang – mills, Nucl. phys. B, 573, 127, (2000) · Zbl 0953.83070 [25] Behrndt, K.; Cvetič, M., Supersymmetric domain wall world from $$D=5$$ simple gauged supergravity, Phys. lett. B, 475, 253, (2000) · Zbl 0961.83064 [26] Seiberg, N.; Witten, E.; Seiberg, N.; Witten, E., Monopoles, duality and chiral symmetry breaking in $$N=2$$ supersymmetric QCD, Nucl. phys. B, Nucl. phys. B, 431, 484, (1994) · Zbl 1020.81911 [27] de Wit, B.; Nicolai, H.; de Wit, B.; Nicolai, H.; Warner, N.P., The embedding of gauged $$N=8$$ supergravity into $$d=11$$ supergravity, Nucl. phys. B, Nucl. phys. B, 255, 29, (1985) [28] Cvetič, M.; Lu, H.; Pope, C.N.; Sadrzadeh, A.; Tran, T.A., Consistent $$SO(6)$$ reduction of type IIB supergravity on $$S5$$, Nucl. phys. B, 586, 275, (2000) · Zbl 1009.83057 [29] Nastase, H.; Vaman, D.; van Nieuwenhuizen, P.; Nastase, H.; Vaman, D.; van Nieuwenhuizen, P., Consistency of the $$AdS7×S4$$ reduction and the origin of self-duality in odd dimensions, Phys. lett. B, Nucl. phys. B, 581, 179, (2000) · Zbl 0985.83026 [30] Nastase, H.; Vaman, D., On the nonlinear KK reductions on spheres of supergravity theories, Nucl. phys. B, 583, 211, (2000) · Zbl 0985.83031 [31] Cvetič, M., Embedding AdS black holes in ten and eleven dimensions, Nucl. phys. B, 558, 96, (1999) · Zbl 0951.83033 [32] Cvetič, M.; Gubser, S.S.; Lu, H.; Pope, C.N., Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories, Phys. rev. D, 62, 086003, (2000) [33] Lu, H.; Pope, C.N.; Tran, T.A., Five-dimensional $$N=4$$, $$SU(2)×U(1)$$ gauged supergravity from type IIB, Phys. lett. B, 475, 261, (2000) · Zbl 0961.83063 [34] Cvetič, M.; Lu, H.; Pope, C.N.; Sadrzadeh, A., Consistency of kaluza – klein sphere reductions of symmetric potentials, Phys. rev. D, 62, 046005, (2000) [35] Chattopadhyay, U.; Karlhede, A., Consistent truncation of kaluza – klein theories, Phys. lett. B, 139, 279, (1984)
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.