Structures in the Gauge/Gravity Duality Cascade

TL;DR

This work probes how corrections to the anomalous mass dimension in the KS Seiberg duality cascade imprint themselves on the gravity side via gauge/gravity duality. By proposing a cascade-dependent form for the anomalous dimension, the authors derive step-like features in the dilaton, NS-NS $B_2$, fluxes, and the warp factor, and show that these features act as gravitational sources for Seiberg duality transitions. The analysis argues that the cascade naturally ends on a baryonic branch rather than confining, with finite step charges accumulating toward the throat bottom. The study also discusses cosmological implications for brane inflation and CMB features, while acknowledging the need for a refined dictionary and a full supergravity solution to capture all corrections. Overall, the paper connects microphysical gauge dynamics to macroscopic geometric structures, offering testable predictions within warped throat scenarios.

Abstract

We study corrections to the anomalous mass dimension and their effects in the Seiberg duality cascade in the Klebanov-Strassler throat, where $\mathcal{N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory with bifundamental chiral superfields and a quartic tree level superpotential in four dimensions is dual to type IIB string theory on $AdS_5 \times T^{1,1}$ background. Analyzing the renormalization group flow of the couplings on the gauge theory side, we propose specific corrections to the anomalous mass dimension. Applying gauge/gravity duality, we then show that the corrections reveal structures on the supergravity side with steps appearing in the running of the fluxes and the metric. The "charges" at the steps provide a gravitational source for Seiberg duality transformations. The finiteness of these corrections suggests that the theory flows to a baryonic branch rather than to a confining branch. The cosmological implication of the duality cascade and the gauge/gravity duality on the brane inflationary scenario and the cosmic microwave background radiation is pointed out.

Figures (4)

• Figure 1: A schematic comparison of the flows of the couplings in $SU(N+M) \times SU(N)$ without the corrections (dashed lines) versus that with the corrections to the anomalous mass dimension (solid lines). Note that a Seiberg duality transition occurs when the flow of $T_{-}(1) =T_{1}(1) -T_{2}(1)$ reaches a period in $b_{2}$.
• Figure 2: Warp factor plotted for parameters $g_s=0.3$, $K=100$, $M=20$, $c=0.0001$ and $r_0=100$.
• Figure 3: A magnified plot of the first step at $r=r_1$ in the warp factor for parameters $g_s=0.3$, $K=5$, $M=20$, $c=0.0001$ and $r_0=100$.
• Figure 4: $D3$-brane potential plotted for parameters $g_s=0.3$, $K=100$, $M=20$, $d=0.0001$ and $r_0=100$.