On the gravity dual of Chern-Simons-matter theories with unquenched flavor

Abstract

We find solutions of type IIA supergravity which are dual to three-dimensional Chern-Simons-matter theories with unquenched fields in the fundamental representation of the gauge group (flavors). In the holographic dual the addition of flavor is performed by means of D6-branes that are extended along the Minkowski gauge theory directions and are delocalized in the internal space in such a way that the system is N = 1 supersymmetric and the flavor group is abelian. For massless flavors the corresponding geometry has the form of a product space AdS 4 × M 6 , where M 6 is a six-dimensional compact manifold whose metric is obtained by squashing the Fubini-Study metric of CP 3 with suitable constant factors which depend on the number of flavors. We compute the effect of dynamical quarks in several observables and, in some cases, we compare our results with the ones corresponding to the N = 3 supergravity solutions generated by localized flavor branes. We also show how to generalize our results to include massive flavors.

Unquenched massive flavors and flows in Chern-Simons matter theories

“…Actually, it was checked in perturbation theory in [24] that the ABJM theory has conformal fixed points even after the addition of flavor. This solution captures rather well many of the effects due to loops of the fundamentals in several observables [23]. Its generalization at non-zero temperature in [16] leads to thermodynamics which pass several non-trivial tests required to a flavored black hole.…”

“…Thus, in the IR limit we expect to find a geometry which reduces to the unflavored ABJM background. On the contrary, when m q → 0, we are in the UV regime and we should recover the deformed Anti-de Sitter background of [23]. The important point to stress here is that the quark mass triggers a non-trivial renormalization group flow between two fixed points and that we can vary m q to enhance or suppress the effects due to the loops of the fundamentals.…”

“…A holographic dual to ABJM with unquenched massless flavors in the Veneziano limit was found in [23]. In this setup the flavor branes fill the AdS 4 and are smeared in the internal CP 3 space in such a way that N = 1 supersymmetry is preserved.…”

“…Notice, that since the flavor branes are not coincident, the flavor symmetry is U(1) N f rather than U(N f ). A remarkable feature of the solution found in [23] is its simplicity and the fact that the tendimensional geometry is of the form AdS 4 × M 6 , where M 6 is a compact six-dimensional manifold whose metric is a squashed version of the unflavored Fubini-Study metric of CP 3 . The radii and squashing factors of this metric depend non-linearly on the flavor deformation parameter N f N λ, where λ = N/k is the 't Hooft coupling of the theory.…”

“…To find the supergravity solutions along the flow, we will adopt an ansatz with brane sources in which the metric and forms are squashed as in [23]. By imposing the preservation of N = 1 supersymmetry, the different functions of the ansatz must satisfy a system of first-order BPS equations, which reduce to a single second-order master equation.…”