Non-supersymmetric Conifold

TL;DR

This work constructs a new one-dimensional family of non-supersymmetric IIB supergravity backgrounds that are holographically dual to the Klebanov–Strassler theory perturbed by specific combinations of relevant single-trace operators and a marginal double-trace operator $U^2$. The authors exploit a decoupling mechanism in which an ISD flux combined with a constant dilaton yields a Ricci-flat, potentially non-Kähler metric on the deformed conifold, enabling simple GKP-type backgrounds with a stable gravity dual. They numerically solve the Papadopoulos–Tseytlin equations to obtain an IR-regular, UV KS-like line of metrics parameterized by $\zeta_1$ and $\zeta_2$, then augment these with ISD flux and a warp factor, fixing the deformation parameter by matching the Maxwell D3-charge to the KS value. Field-theory interpretation identifies the dual as KS perturbed by gaugino masses and a baryon-number-related operator $U$, along with a marginal double-trace term $U^2$, with the background remaining perturbatively stable for small $\zeta_1$ and long-lived non-SUSY vacua nonperturbatively. The results provide a tractable holographic setting to study non-supersymmetric confining dynamics with a simple geometric structure and potential applications to baryonic matter models and string-inspired cosmology.

Abstract

We find a new family of non-supersymmetric numerical solutions of IIB supergravity which are dual to the N=1 cascading "conifold" theory perturbed by certain combinations of relevant single trace and marginal double trace operators with non infinitesimal couplings. The SUSY is broken but the resulting ground states, and their gravity duals, remain stable, at least perturbatively.Despite the complicated field theory dynamics the gravity solutions have a simple structure. They feature the Ricci-flat non-Kahler metric on the deformed conifold and the imaginary self-dual three-form flux accompanied by a constant dilaton.

Figures (6)

• Figure 1: We define ${\mathcal{M}}_U$ as a space of combinations of relevant/marginal couplings -- and the corresponding theories -- such that the bottom component of the $U(1)_{\rm baryon}$ multiplet has the vacuum value $U$. Schematically we denote $x$ to be the coordinates on ${\mathcal{M}}_U$ (we do not specify the dimension of ${\mathcal{M}}_U$) such that $x=0$ corresponds to the unperturbed ${\mathcal{N}=1}$ theory. Red dashed line corresponds to the motion in the space of theories starting from the unperturbed ${\mathcal{N}=1}$ theory such that vev $U$ stays constant. Most of these theories have complicated gravity dual. At a specific point the gravity dual accidently becomes simpler -- it is of GKP type. The one-dimensional family of such theories forms the thin blue line. These are the theories we study.
• Figure 2: The red points show the values of $\zeta_1$ and $\zeta_2$ for which the Ricci-flat metric is regular in both the IR and the UV. Notice that the points near the origin lie on the parabola (the blue line). The deviation of the points with larger $\zeta_1$ from the parabola most likely indicates the contribution of the $\zeta_1^4$ term in (\ref{['familyc']}).
• Figure 3: The four lines show numerical solutions for $e^{10 p (\tau)}, 1/\dot{q}(\tau), e^{y (\tau)}$ and $z(\tau)$ for $(\zeta_1, \zeta_2) = (0.193(9), 0.009)$ (the last point on the previous plot).
• Figure 4: The blue solid line show the numerical result for $e^{y (\tau)}$ with $(\zeta_1, \zeta_2) = (0.193(9), 0.009)$, while the red dashed line corresponds to $e^{y_0 (\tau)} = \tanh(\frac{\tau}{2})$ of the conventional deformed conifold of candelas. Notice that red line converges to the asymptotic faster than the blue line. This is so because for large $\tau$ the function $1-e^{y(\tau)}$ goes like $e^{-\tau}$ for the the deformed conifold, and as $e^{-\tau/3}$ for our solution.
• Figure 5: The solid blue and the dashed red lines correspond to the numeric solution for $F(\tau)$ with $\zeta_1 = 0.193(9)$ and the same function in the KS geometry, respectively.