The supergravity dual of 3Dsupersymmetric gauge theories with unquenched flavors

Abstract

We obtain the supergravity dual of N = 1 gauge theory in 2+1 dimensions with a large number of unquenched massless flavors. The geometries found are obtained by solving the equations of motion of supergravity coupled to a suitable continuous distribution of flavor branes. The background obtained preserves two supersymmetries. We find that when N c ≥ 2N f the behavior of the solutions is compatible with having an asymptotically free dual gauge theory with dynamical quarks. On the contrary, when N c < 2N f the theory develops a Landau pole in the UV. We also find a new family of (unflavored) backgrounds generated by D5-branes that wrap a three-cycle of a cone with G 2 holonomy. 1 canoura@fpaxp1.usc.es 2 merlatti@fpaxp1.usc.es 3 alfonso@fpaxp1.usc.es

Non-Abelian T-duality, G 2-structure rotation and holographic duals of $ \mathcal{N} $ = 1 Chern-Simons theories

“…where ǫ only depends on r (Appendix B of [4] provides further details). Thus one expects the non-abelian T-dual of wrapped D5 branes on Σ 3 to preserve N = 1 SUSY.…”

“…The field theory living on the world volume of these branes is only effectively 3-d in the IR and so the geometry is only a good description of the low energy dynamics of SYM in 3-d. A UV completion is provided by another solution generating technique, G 2 -structure rotation [5], which is analogous to U-duality. This acts on the S-dual of a deformation of the Maldacena and Nastase solution [4] and maps it to a geometry supporting D2 and fractional D2 branes that asymptotes to AdS 4 × Y in the UV and is the G 2 analogue of the baryonic branch of Klebanov-Strassler [32]. The compact metric Y has finite volume in the UV and so the fractional branes which wrap cycles in Y remain effectively 3-d in the whole geometry.…”

“…In this work a new type-IIA SuGra solution, dual to a confining gauge theory in 3-d, is generated by performing a T-duality along one of the SU (2) isometries of the deformed Maldacena-Nastase solution [4]. This new solution preserves N = 1 SUSY in the form of a dynamic SU(3)-structure in 7-d [28,29].…”

“…The analysis of the deformed Maldacena-Nastase and its G 2 -structure rotation is mostly a review of what can be found in [3,4,6,35] although additional clarifications are made. In particular further details of a Seiberg like duality in the G 2 -structure rotated solution are given and how this effects the Chern-Simons level, the proposal for which is new.…”

“…The purpose of this section is to review its deformation due to Canoura, Merlatti and Ramallo [4], as this constitutes more general ansatz to a set of wrapped D5 brane solutions [4-6, 35, 36] which contain the Maldacena-Nastase solution as a special case 1 . The string frame metric is given by:…”