Confinement and D5 branes

TL;DR

The work constructs and analyzes new Type IIB backgrounds built from wrapped D5 branes to realize confining QFTs in both 4+1 and 2+1 dimensions, with ultraviolet dynamics governed by Little String Theory. It systematically computes holographic observables—gauge couplings, Wilson and 't Hooft loops, entanglement entropy, density of states, and spin-two glueball spectra—to characterize confinement, screening, and the presence of a mass gap, as well as the discrete-to-continuum transitions in the spectra controlled by geometric and flux parameters. A parallel set of results for black membrane solutions extends the analysis to finite-temperature (thermodynamic) regimes, using Noether-Wald charges and careful boundary terms to discuss mass, entropy, and temperature, along with the role of counterterms. The paper also compares SUSY-preserving mechanisms (twisting vs Wilson lines) and clusters backgrounds by the fate of wrapped cycles, offering a geometric taxonomy of confining holographic duals and signaling several avenues for further exploration in higher-dimensional and meron-augmented backgrounds.

Abstract

In this work we present new solutions of type IIB supergravity based on wrapped D5 branes. We propose that two of these backgrounds are holographically dual to Quantum Field Theories that confine. The high energy regime of the field theories is that of a Little String Theory. We study various observables (Wilson and 't Hooft loops, Entanglement entropy, density of degrees of freedom and the spectrum of spin-two glueballs, among others). We also present two new black membrane backgrounds and analyse some thermodynamic aspects of these solutions.

Figures (6)

• Figure 1: Behaviour of the string coupling constant (blue) and the Ricci scalar (red) as a function of the holographic coordinate. The two scales of the theory are depicted: at $r=r_{+}$ the compactification circle is effectively of zero size and the theory is (4+1)-dimensional. When the string coupling constant becomes of order one, we S-dualise and the theory is described in terms of the NS5-brane.
• Figure 2: Left: Parametric plot of $E_{QQ}(L_{QQ})$ in the BPS bound $m=0$. Bottom Right: the profiles of different strings as they explore the bulk. The longer the separation $L_{QQ}$, the more the string approaches $\frac{r_{0}}{r_{+}}\sim 1$. This is usual of the backgrounds dual to a confining QFT behaviour.
• Figure 3: The integrals of the monopole-antimonopole t' Hooft loop \ref{['energylengththooft']} can be written in terms of two parameters $\lambda=-r_{-}^2/r_{+}^2$ and $N$. All the plots are considering $\lambda=2.5$ and $N=3$. Upper left: Plot comparing the exact expression for the monopole separation \ref{['energylengththooft']} with the approximate expression $\hat{L}_{MM}$ in \ref{['lappthoft']}. Upper right: The energy of the t'Hooft loop as a function of the $r_0$ in units of $r_+$. Bottom left: Different profiles of the macroscopic strings as a function of the turn-around point $r_0$. Bottom Left: Plot of the function $E_{MM}(L_{MM})$. The upwards concavity ascertains the prediction that the embedding is unstable.
• Figure 4: Glueball profile for a particular configuration $\lambda=6,N=1,n=1$. Left: Radial profile for the three allowed values of $p=0,1,2.$. Right: In black the Schroedinger effective potential \ref{['schrodinger effective potential bg1']} and in colors the value of the glueball masses associated to the excitations $p=0,1,2$.
• Figure 5: The integrals of the quark-antiquark Wilson loop \ref{['integrals background2 wilsonloop']}. Upper left: Plot comparing the exact expression for the monopole separation \ref{['integrals background2 wilsonloop']} with the approximate expression $\hat{L}_{QQ}$ in \ref{['Lapp background2 wilsonloop']}. Upper right: The energy of the Wilson loop as a function of the $r_0$. Bottom left: Different profiles of the macroscopic strings as a function of the turn-around point $r_0$. Bottom Left: Plot of the function $E_{QQ}(L_{QQ})$.