The heterotic perturbative vacua in string geometry theory

TL;DR

The paper embeds heterotic perturbative vacua into string geometry theory by parameterizing backgrounds with $G_{ m\mu\nu}(x)$, $B_{ m\mu\nu}(x)$, $\phi(x)$, and $A_{\mu}(x)$ and deriving their perturbative heterotic string path integrals to all orders in $\hbar$. It shows how Weyl (super-Weyl) invariance selects backgrounds consistent with heterotic supergravity and computes a nonperturbative, background-sensitive framework that yields $S_s$ as the worldsheet action for heterotic strings on these vacua. A classical potential $V_{ m string}$ is constructed by substituting the vacua into the string-geometry action and enforcing background equations via Lagrange multipliers, with Einstein-frame and warped-compactification reductions to enable phenomenological analysis. The work posits that the global minimum of the background potential across heterotic (and other) sectors determines the true vacuum of string theory, providing a route to connect nonperturbative string geometry to four-dimensional physics and cosmology. This framework lays the groundwork for identifying the true heterotic vacuum and for exploring Standard Model-like physics emerging from fluctuations around it.

Abstract

String geometry theory is one of the candidates of the non-perturbative formulation of superstring theory. In this paper, in string geometry theory, we identify perturbative heterotic vacua, which include general heterotic backgrounds. From fluctuations around these vacua, we derive the path-integrals of heterotic perturbative superstrings on the backgrounds up to any order.

Figures (2)

• Figure 1: Various string states. The red and blue lines represent one string and two strings, respectively.
• Figure 2: A path and a super Riemann surface. The line on the left is a trajectory in the path integral. The trajectory parametrized by $\bar{\tau}$ from $-\infty$ to $\infty$, represents a super Riemann surface with fixed punctures in $\mathcal{M}$ on the right.