Abstract
We construct analytically the gravity duals of three-dimensional, super Yang-Mills-type theories with \( \mathcal{N}=1 \) supersymmetry coupled to N f quark flavors. The backreaction of the quarks on the color degrees of freedom is included, and corresponds on the gravity side to the backreaction of N f D6-branes on the background of N D2-branes. The D6-branes are smeared over the compact part of the geometry, which must be a six-dimensional nearly Kähler manifold in order to preserve supersymmetry. For massless quarks, the solutions flow in the IR to an AdS4 fixed point dual to a Chern-Simons-matter theory. For light quarks the theories exhibit quasi-conformal dynamics (walking) at energy scales m q ≪ E ≪ λN f /N, with λ = gYM2N the ’t Hooft coupling.
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References
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
B.S. Acharya, J.M. Figueroa-O’Farrill, C.M. Hull and B.J. Spence, Branes at conical singularities and holography, Adv. Theor. Math. Phys. 2 (1999) 1249 [hep-th/9808014] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
O. Pelc and R. Siebelink, The D2-D6 system and a fibered AdS geometry, Nucl. Phys. B 558 (1999) 127 [hep-th/9902045] [INSPIRE].
S.A. Cherkis and A. Hashimoto, Supergravity solution of intersecting branes and AdS/CFT with flavor, JHEP 11 (2002) 036 [hep-th/0210105] [INSPIRE].
M. Gomez-Reino, S.G. Naculich and H. Schnitzer, Thermodynamics of the localized D2-D6 system, Nucl. Phys. B 713 (2005) 263 [hep-th/0412015] [INSPIRE].
J. Erdmenger and I. Kirsch, Mesons in gauge/gravity dual with large number of fundamental fields, JHEP 12 (2004) 025 [hep-th/0408113] [INSPIRE].
F. Bigazzi, R. Casero, A.L. Cotrone, E. Kiritsis and A. Paredes, Non-critical holography and four-dimensional CFT’s with fundamentals, JHEP 10 (2005) 012 [hep-th/0505140] [INSPIRE].
C. Núñez, A. Paredes and A.V. Ramallo, Unquenched Flavor in the Gauge/Gravity Correspondence, Adv. High Energy Phys. 2010 (2010) 196714 [arXiv:1002.1088] [INSPIRE].
E. Conde and A.V. Ramallo, On the gravity dual of Chern-Simons-matter theories with unquenched flavor, JHEP 07 (2011) 099 [arXiv:1105.6045] [INSPIRE].
H. Ooguri and C.-S. Park, Superconformal Chern-Simons Theories and the Squashed Seven Sphere, JHEP 11 (2008) 082 [arXiv:0808.0500] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
N. Seiberg, Notes on theories with 16 supercharges, Nucl. Phys. Proc. Suppl. 67 (1998) 158 [hep-th/9705117] [INSPIRE].
A. Gray and L.M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. 123 (1980) 35.
P.A. Nagy, NK geometry and Riemannian foliations, Asian J. Math. 6 (2002) 481 [math.DG/0203038].
R. Grunewald, Six-dimensional Riemannian manifolds with a real Killing spinor, Ann. Global Anal. Geom. 8 (1990) 43.
C. Bär, Real Killing spinors and holonomy, Comm. Math. Phys. 154 (1993) 509.
M. Atiyah and E. Witten, M theory dynamics on a manifold of G2 holonomy, Adv. Theor. Math. Phys. 6 (2003) 1 [hep-th/0107177] [INSPIRE].
B.S. Acharya and E. Witten, Chiral fermions from manifolds of G2 holonomy, hep-th/0109152 [INSPIRE].
K. Behrndt and M. Cvetič, General N = 1 supersymmetric flux vacua of (massive) type IIA string theory, Phys. Rev. Lett. 95 (2005) 021601 [hep-th/0403049] [INSPIRE].
K. Behrndt and M. Cvetič, General N = 1 supersymmetric fluxes in massive type IIA string theory, Nucl. Phys. B 708 (2005) 45 [hep-th/0407263] [INSPIRE].
S. Chiossi and S. Salamon, The Intrinsic torsion of SU(3) and G2 structures, J. Diff. Geom. (2002) [math/0202282] [INSPIRE].
M. Verbitsky, An intrinsic volume functional on almost complex 6-manifolds and NK geometry, Pacific J. Math. 235 (2008) 323.
C.P. Boyer and K. Galicki, Sasakian geometry, holonomy and supersymmetry, math/0703231 [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Bianchi IX selfdual Einstein metrics and singular G2 manifolds, Class. Quant. Grav. 20 (2003) 4239 [hep-th/0206151] [INSPIRE].
K. Behrndt, G. Dall’Agata, D. Lüst and S. Mahapatra, Intersecting six-branes from new seven manifolds with G2 holonomy, JHEP 08 (2002) 027 [hep-th/0207117] [INSPIRE].
M. Fernandez, S. Ivanov, V. Muñoz and L. Ugarte, Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities, math/0602160 [INSPIRE].
J.B. Butruille, Homogeneous NK manifolds, math.DG/0612655.
A. Loewy and Y. Oz, Branes in special holonomy backgrounds, Phys. Lett. B 537 (2002) 147 [hep-th/0203092] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].
B.S. Acharya, F. Denef, C. Hofman and N. Lambert, Freund-Rubin revisited, hep-th/0308046 [INSPIRE].
F. Benini, F. Canoura, S. Cremonesi, C. Núñez and A.V. Ramallo, Unquenched flavors in the Klebanov-Witten model, JHEP 02 (2007) 090 [hep-th/0612118] [INSPIRE].
D. Cassani and A.-K. Kashani-Poor, Exploiting N = 2 in consistent coset reductions of type IIA, Nucl. Phys. B 817 (2009) 25 [arXiv:0901.4251] [INSPIRE].
M. Haack, D. Lüst, L. Martucci and A. Tomasiello, Domain walls from ten dimensions, JHEP 10 (2009) 089 [arXiv:0905.1582] [INSPIRE].
J. Gutowski, G. Papadopoulos and P.K. Townsend, Supersymmetry and generalized calibrations, Phys. Rev. D 60 (1999) 106006 [hep-th/9905156] [INSPIRE].
P. Koerber and D. Tsimpis, Supersymmetric sources, integrability and generalized-structure compactifications, JHEP 08 (2007) 082 [arXiv:0706.1244] [INSPIRE].
D. Lüst and D. Tsimpis, Supersymmetric AdS4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [INSPIRE].
J. Gaillard and J. Schmude, The Lift of type IIA supergravity with D6 sources: M-theory with torsion, JHEP 02 (2010) 032 [arXiv:0908.0305] [INSPIRE].
T. Appelquist and D. Nash, Critical Behavior in (2+1)-dimensional QCD, Phys. Rev. Lett. 64 (1990) 721 [INSPIRE].
J. Polchinski, Introduction to Gauge/Gravity Duality, arXiv:1010.6134 [INSPIRE].
A.J. Niemi and G.W. Semenoff, Axial Anomaly Induced Fermion Fractionization and Effective Gauge Theory Actions in Odd Dimensional Space-Times, Phys. Rev. Lett. 51 (1983) 2077 [INSPIRE].
A.N. Redlich, Gauge Noninvariance and Parity Violation of Three-Dimensional Fermions, Phys. Rev. Lett. 52 (1984) 18 [INSPIRE].
A.N. Redlich, Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions, Phys. Rev. D 29 (1984) 2366 [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-Theorem: N = 2 Field Theories on the Three-Sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
J. Gutowski, S. Ivanov and G. Papadopoulos, Deformations of generalized calibrations and compact nonKähler manifolds with vanishing first Chern class, math/0205012 [INSPIRE].
P. Koerber and L. Martucci, D-branes on AdS flux compactifications, JHEP 01 (2008) 047 [arXiv:0710.5530] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].
J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge / gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP 05 (2007) 067 [hep-th/0701132] [INSPIRE].
A.F. Faedo, A. Kundu, D. Mateos, C. Pantelidou and J. Tarrio, Super Yang-Mills with Compressible Quark Matter, to appear.
A.F. Faedo, A. Kundu, D. Mateos and J. Tarrio, (Super) Yang-Mills at Finite Heavy-Quark Density, JHEP 02 (2015) 010 [arXiv:1410.4466] [INSPIRE].
A.-K. Kashani-Poor, Nearly Kähler Reduction, JHEP 11 (2007) 026 [arXiv:0709.4482] [INSPIRE].
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Faedo, A.F., Mateos, D. & Tarrío, J. Three-dimensional super Yang-Mills with unquenched flavor. J. High Energ. Phys. 2015, 56 (2015). https://doi.org/10.1007/JHEP07(2015)056
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DOI: https://doi.org/10.1007/JHEP07(2015)056