Perturbative Gauge Theory and Closed String Tachyons

TL;DR

The paper uncovers a precise one-to-one map between perturbative large-$N$ orbifold gauge theories on D3-branes at the tip of $\mathbb{R}^6/\Gamma$ and the spectrum of twisted-sector tachyons in free closed strings on $\mathbb{R}^{3,1}\times \mathbb{R}^6/\Gamma$. It shows that the stability of double-trace deformations in the gauge theory, encoded by the discriminant $D = \gamma_O^2 - a_O v_O$ and related beta-function structure, mirrors the presence or absence of tachyons in twisted string sectors; supersymmetric cases yield fixed lines $f=-\lambda$ and non-supersymmetric cases exhibit no such fixed lines. The work provides a concrete, calculable gauge/string correspondence in the absence of RR backgrounds and demonstrates a no-go theorem ruling out conformal non-supersymmetric orbifolds at one loop. It also connects tree-level and one-loop contributions via $U(1)$ factors, abelian orbifold generalizations, and zero-point energy analyses, offering a framework to study twisted-sector tachyon condensation from the gauge theory perspective.

Abstract

We find an interesting connection between perturbative large N gauge theory and closed superstrings. The gauge theory in question is found on N D3-branes placed at the tip of the cone R^6/Gamma. In our previous work we showed that, when the orbifold group Gamma breaks all supersymmetry, then typically the gauge theory is not conformal because of double-trace couplings whose one-loop beta functions do not possess real zeros. In this paper we observe a precise correspondence between the instabilities caused by the flow of these double-trace couplings and the presence of tachyons in the twisted sectors of type IIB theory on orbifolds R^{3,1}x R^6/Gamma. For each twisted sectors that does not contain tachyons, we show that the corresponding double-trace coupling flows to a fixed point and does not cause an instability. However, whenever a twisted sector is tachyonic, we find that the corresponding one-loop beta function does not have a real zero, hence an instability is likely to exist in the gauge theory. We demonstrate explicitly the one-to-one correspondence between the regions of stability/instability in the space of charges under Gamma that arise in the perturbative gauge theory and in the free string theory. Possible implications of this remarkably simple gauge/string correspondence are discussed.

Figures (4)

• Figure 1: Stability/instability regions for general abelian orbifolds
• Figure 2: The (rescaled) singlet discriminant and the closed string zero-point energy. Both are negative in the same range of $x$.
• Figure 3: The (rescaled) eigenvalue ${\cal M}_{1}^d$ and the closed string zero-point energy, plotted as a function of $x$. Both are negative (the solid line portions of the two curves) in the same range of $x$.
• Figure 4: The (rescaled) eigenvalues of the discriminant matrix, the smallest eigenvalue (continuous line) and the closed string zero-point energy as a function of normalized twisted sector charge $x$ for an $SU(2)$-symmetric orbifold. The crossing of eigenvalues as a function of charge is cricial for the successful match of gauge theory and string theory instabilities.