New supergravity backgrounds dual to 𝒩 = 1 SQCD-like theories withN_f= 2N_c

Abstract

We present new supergravity backgrounds generated by N c D5-branes, wrapping the S 2 of the resolved conifold, in the presence of N f = 2N c smeared flavor D5-branes. The smearing allows us to take their backreaction on the geometry into account. We discuss the consistency, stability, and supersymmetry of these types of setups. We find near horizon geometries that we expect to be supergravity duals of SQCD-like theories with N f = 2N c . From these backgrounds we numerically extract rectangular Wilson loops and beta functions of the dual field theory for the regime where our approximations are valid.

Remarks on the string dual toN=1supersymmetric QCD

“…The new solution leads to an asymptotic UV geometry of the form R 1,3 × M 6 , where M 6 is the conifold. Such UV asymptotics was anticipated in [16] and the solution (4.7) is the first exact example possessing this UV behavior. The physics of this and other solutions with similar UV behavior will be analyzed in Section 5.…”

“…We then compute the eq. of motion for the gauge field, obtaining 16) where Θ 0 is an integration constant. Replacing back into the action (5.15), we get 17) which is the action for an 'effective string' that is what we consider to be the QCD string (for dyons), with tension given by…”

Stability of non-extremal conifold backgrounds with sources

“…Note that, unlike more standard finite temperature solutions where the non-extremality factor e −8x enters only in the g rr and g tt elements of the metric, here the warp factor H and the fluxes F (5) and H (3) depend on e −8x . 10 The use of U-dualities is a well stablished solution generating technique in supergravity. In the presence of smeared flavored branes one could question the validity and meaning of the uplift to eleven dimensions.…”

“…where the variation of the Chern-Simons term in the bulk action is cancelled by the variation of the Wess-Zumino term in the source action. Here, T sources µν is obtained from (after rotation) T µν sources = 2κ 2 10 √ −g (10) δL sources δg µν , (4.13) and has components: Again, the Einstein equations can be checked to hold given the EOMs before rotation.…”

“…In order to incorporate dynamical flavor in the fundamental representation in these backgrounds we have to consider the backreaction of flavor branes. This difficult problem can be tackled using a smearing technique and has been extensively explored in the literature [8][9][10][11][12][13][14].…”