New Type IIB Backgrounds and Aspects of Their Field Theory Duals

TL;DR

This work constructs new Type IIB backgrounds by applying non-Abelian T-duality to Type IIA solutions engineered from reductions of $G_2$-holonomy manifolds, revealing a dynamical $SU(2)$ structure in the dual geometry. The authors explicitly solve the IIA BPS system (including semi-analytic, stabilized-dilaton solutions) and analyze the resulting IIB backgrounds, fluxes, and calibrations, deriving SUSY conditions with pure-spinor formulations. They study the dual four-dimensional field theories, finding confinement-like IR behavior accompanied by non-local UV characteristics that require a UV completion, and propose a two-node quiver inferred from Page charges. Central charges and entanglement entropy are computed to characterize the non-local QFTs, while domain walls, Wilson/'t Hooft loops, and gauge couplings provide IR diagnostics and constraints on the dual QFT data. The results offer a concrete avenue to explore non-Abelian T-duality in backgrounds with reduced supersymmetry and illuminate the structure of their strongly coupled duals.

Abstract

In this paper we study aspects of geometries in Type IIA and Type IIB String theory and elaborate on their field theory dual pairs. The backgrounds are associated with reductions to Type IIA of solutions with $G_2$ holonomy in eleven dimensions. We classify these backgrounds according to their G-structure, perform a non-Abelian T-duality on them and find new Type IIB configurations presenting {\it dynamical} $SU(2)$-structure. We study some aspects of the associated field theories defined by these new backgrounds. Various technical details are clearly spelled out.

Figures (6)

• Figure 1: $e^{\frac{4 \phi }{3}}$ for different values of $q_0$ and $R_0$. We keep $q_0 R_0 =2$ fixed which amounts to fixing the normalization of the dilaton in the IR.
• Figure 2: A numerical solution for $a(r), b(r), c(r)$ and $f(r)$ obtained by forward integration of the BPS equations with \ref{['eq:Dat0-bis']} as boundary conditions, $R_0=10,$ and $q_0=1/5$. After the minimization procedure explained in the appendix \ref{['appendix-numerics']} we find that for the UV parameters $q_1 =1.31946 ,\ R_1= -2.03087,\ h_1 =−1.9733$ this solution has the required UV behavior \ref{['eq:sol-UV']}. We also plot $h(r)^2$ and $e^{4\phi/3}$ defined in \ref{['metricxxx']}
• Figure 3: Solid line: $\alpha(r)$ for the numerical solution with $R_0=10$, $q_0= 1/5$. Dashed line: $\alpha(r)$ for the exact solution of eq.\ref{['eq:exactsol']}, $\alpha_{exact}(r)=\frac{1}{2}$
• Figure 4: The central charge for a numerical solution with stabilized dilaton (red dashed curve) and for the exact solution with linear dilaton (green curve).
• Figure 5: The blue curves are the result of forward integration with $R_0=10,\ q_0=1/5$. After the minimization procedure we obtain the UV parameters $q_1 = 1.31946,\ R_1= -2.03087,\ h_1 = -1.9733$ and plot (dashed red lines) the result of integrating back with these parameters to show that it coincides with the forward integration. The small discrepancies in the IR are due to accumulated numerical error. The mismatch function for this solution is $m < 10^{-4}$. We also plot $h(r)^2$ and $e^{4\phi/3}$ defined in \ref{['metricxxx']}