Abstract
We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I′ by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7’s. The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring. Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background.
This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I′, namely of the \( \mathcal{N} = 2 \) Sp(1) SYM theory with N f = 4. Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory. They also explain the recent observation that the exact coupling for this theory can be entirely reconstructed from its perturbative part plus the knowledge of the chiral ring on the D7 branes supporting its flavor degrees of freedom.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
A.M. Polyakov, The wall of the cave, Int. J. Mod. Phys. A 14 (1999) 645 [hep-th/9809057] [SPIRES].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [SPIRES].
J.M. Maldacena and C.Núñez, Towards the large-N limit of pure N = 1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [SPIRES].
N. Seiberg and E. Witten, Monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [hep-th/9407087] [SPIRES].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [SPIRES].
I.R. Klebanov and N.A. Nekrasov, Gravity duals of fractional branes and logarithmic RG flow, Nucl. Phys. B 574 (2000) 263 [hep-th/9911096] [SPIRES].
M. Bertolini et al., Fractional D-branes and their gauge duals, JHEP 02 (2001) 014 [hep-th/0011077] [SPIRES].
J. Polchinski, N = 2 gauge/gravity duals, Int. J. Mod. Phys. A 16 (2001) 707 [hep-th/0011193] [SPIRES].
M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda and R. Marotta, N = 2 gauge theories on systems of fractional D3/D7 branes, Nucl. Phys. B 621 (2002) 157 [hep-th/0107057] [SPIRES].
M. Billó, L. Gallot and A. Liccardo, Classical geometry and gauge duals for fractional branes on ALE orbifolds, Nucl. Phys. B 614 (2001) 254 [hep-th/0105258] [SPIRES].
P. Di Vecchia, A. Liccardo, R. Marotta and F. Pezzella, On the gauge/gravity correspondence and the open/closed string duality, Int. J. Mod. Phys. A 20 (2005) 4699 [hep-th/0503156] [SPIRES].
C.V. Johnson, A.W. Peet and J. Polchinski, Gauge theory and the excision of repulson singularities, Phys. Rev. D 61 (2000) 086001 [hep-th/9911161] [SPIRES].
M. Petrini, R. Russo and A. Zaffaroni, N = 2 gauge theories and systems with fractional branes, Nucl. Phys. B 608 (2001) 145 [hep-th/0104026] [SPIRES].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [SPIRES].
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [SPIRES].
M.B. Green and M. Gutperle, D-instanton induced interactions on a D3-brane, JHEP 02 (2000) 014 [hep-th/0002011] [SPIRES].
M. Billó et al., Classical gauge instantons from open strings, JHEP 02 (2003) 045 [hep-th/0211250] [SPIRES].
M.B. Green and M. Gutperle, Effects of D-instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [SPIRES].
M.B. Green and M. Gutperle, D-particle bound states and the D-instanton measure, JHEP 01 (1998) 005 [hep-th/9711107] [SPIRES].
M.B. Green and M. Gutperle, D-instanton partition functions, Phys. Rev. D 58 (1998) 046007 [hep-th/9804123] [SPIRES].
E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030] [SPIRES].
M.R. Douglas, Branes within branes, hep-th/9512077 [SPIRES].
G.W. Moore, N. Nekrasov and S. Shatashvili, D-particle bound states and generalized instantons, Commun. Math. Phys. 209 (2000) 77 [hep-th/9803265] [SPIRES].
U. Bruzzo, F. Fucito, J.F. Morales and A. Tanzini, Multi-instanton calculus and equivariant cohomology, JHEP 05 (2003) 054 [hep-th/0211108] [SPIRES].
R. Flume and R. Poghossian, An algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential, Int. J. Mod. Phys. A 18 (2003) 2541 [hep-th/0208176] [SPIRES].
M. Billó et al., Exotic instanton counting and heterotic/type-I’ duality, JHEP 07 (2009) 092 [arXiv:0905.4586] [SPIRES].
F. Fucito, J.F. Morales and R. Poghossian, Exotic prepotentials from D(−1)D7 dynamics, JHEP 10 (2009) 041 [arXiv:0906.3802] [SPIRES].
M. Billó et al., Stringy instanton corrections to N = 2 gauge couplings, JHEP 05 (2010) 107 [arXiv:1002.4322] [SPIRES].
M. Billó, L. Gallot, A. Lerda and I. Pesando, F-theoretic vs microscopic description of a conformal N = 2 SYM theory, JHEP 11 (2010) 041 [arXiv:1008.5240] [SPIRES].
A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [SPIRES].
T. Banks, M.R. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett. B 387 (1996) 278 [hep-th/9605199] [SPIRES].
J.H. Schwarz, Covariant field equations of chiral N = 2 D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [SPIRES].
P.S. Howe and P.C. West, The complete N = 2, D = 10 supergravity, Nucl. Phys. B 238 (1984) 181 [SPIRES].
S. de Haro, A. Sinkovics and K. Skenderis, A supersymmetric completion of the R 4 term in IIB supergravity, Phys. Rev. D 67 (2003) 084010 [hep-th/0210080] [SPIRES].
M.B. Green and C. Stahn, D3-branes on the Coulomb branch and instantons, JHEP 09 (2003) 052 [hep-th/0308061] [SPIRES].
J. Polchinski, Dirichlet-Branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [SPIRES].
P. Di Vecchia et al., Classical p-branes from boundary state, Nucl. Phys. B 507 (1997) 259 [hep-th/9707068] [SPIRES].
M.B. Green, J.H. Schwarz and E. Witten, Superstring theory. Vol. 2: Loop amplitudes, anomalies and phenomenology, Cambridge University Press, Cambridge U.K. (1987) [SPIRES].
M. Billó, M. Frau, L. Gallot, A. Lerda and I. Pesando, Classical solutions for exotic instantons?, JHEP 03 (2009) 056 [arXiv:0901.1666] [SPIRES].
B. Grossman, T.W. Kephart and J.D. Stasheff, Solutions to gauge field equations in eight-dimensions: conformal invariance and the last Hopf map, Phys. Lett. B 220 (1989) 431 [SPIRES].
B. Grossman, T.W. Kephart and J.D. Stasheff, Solutions to Yang-Mills field equations in eight-dimensions and the last Hopf map, Commun. Math. Phys. 96 (1984) 431 [Erratum ibid. 100 (1985) 311] [SPIRES].
J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) 6041 [hep-th/9407031] [SPIRES].
M. Billó, M. Frau, F. Fucito and A. Lerda, Instanton calculus in R-R background and the topological string, JHEP 11 (2006) 012 [hep-th/0606013] [SPIRES].
K. Ito et al., N = 2 instanton effective action in omega-background and D3/D(−1)-brane system in R-R background, JHEP 11 (2010) 093 [arXiv:1009.1212] [SPIRES].
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ArXiv ePrint: 1105.1869
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Billó, M., Frau, M., Giacone, L. et al. Holographic non-perturbative corrections to gauge couplings. J. High Energ. Phys. 2011, 7 (2011). https://doi.org/10.1007/JHEP08(2011)007
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DOI: https://doi.org/10.1007/JHEP08(2011)007