Holographic observables in TsT deformations of confining theories

TL;DR

We construct four type-IIB backgrounds by applying TsT transformations to the uplift of the Anabalón–Nastase–Oyarzo soliton, yielding two marginal and two dipole deformations. We compute Page charges, Wilson loops, 't Hooft loops, entanglement entropy, and holographic central charge flow to compare UV and RG features across the deformed geometries, revealing a universal factorisation for marginal deformations and a gamma-dependent Wilson-loop structure for dipoles. For marginal deformations, we find $Q_{D3}=N$ with an additional $Q_{D5}=\gamma N$ (requiring $\gamma\in\mathbb{Q}$ for flux quantization) and an invariant $c_{\text{flow}}$ with $c_{\text{UV}}=N$, $c_{\text{IR}}=0$, reproducing seed results. Dipole deformations keep the seed Page charges but induce explicit $\gamma$-dependence in Wilson loops (wedge at small separation and linear confinement at large distance) and require a generalized central-charge prescription due to coordinate-dependent $c_{\text{flow}}$, highlighting distinct UV/IR modifications in these non-commutative-like backgrounds.

Abstract

We construct new families of type-IIB supergravity solutions by employing TsT transformations on the ten-dimensional geometry that arises after the uplift of the five-dimensional soliton solution of Anabalón, Nastase, and Oyarzo. In particular, we identify two marginal and two dipole deformations of the uplifted geometry. We then analyse a plethora of holographic observables -- including Wilson loops, `t~Hooft loops, Page charges, entanglement entropy, and central charge -- and compare their behaviour across the different deformed backgrounds.

Figures (10)

• Figure 1: The separation length as a function of the turning point, and the quark-anti-quark potential as a function of the separation, for different values of $\hat{\nu}$. For simplicity we set $L = \ell = 1$. The figures at the top correspond to the embedding with $\theta_0 = 0$, while the ones at the bottom to the embedding with $\theta_0 = \frac{\pi}{2}$.
• Figure 2: The energy as a function of the separation when $\theta_0 = 0$ and $\hat{\nu}$ takes values near $-1$. The triangle disappears near $\hat{\nu} \simeq - 0.95$. For simplicity we set $L = \ell = 1$.
• Figure 3: The quark-anti-quark separation as a function of the turning point when $\theta_0 = 0$ and $\psi_0 = \pi/2$. Each figure corresponds to a different value of $\hat{\nu}$ and each curve to a different value of $\gamma$. For simplicity we set $L = \ell = 1$.
• Figure 4: The energy as a function of the separation when $\theta_0 = 0$ and $\psi_0 = \pi/2$. Each figure corresponds to a different value of $\hat{\nu}$ and each curve to a different value of $\gamma$. For simplicity we set $L = \ell = 1$.
• Figure 5: Zoom-ins of Fig. \ref{['fig:dipoleIenergyWLimage1']}(left) and Fig. \ref{['fig:dipoleIenergyWLimage4']}(right) reveal the triangular shape.