M-theory on $S^1\vee S^1$ as Type 0A

TL;DR

This paper proposes a novel M-theory dual for Type 0A string theory involving compactification on a connected sum of two circles, exploring dualities, tachyon condensation, and implications for non-supersymmetric gauge theories.

Contribution

It introduces an exotic geometric dual involving a connected sum of circles, linking tachyon dynamics to dualities and proposing a new strong coupling fixed point in non-supersymmetric gauge theories.

Findings

Tachyon condensation corresponds to shrinking one circle, leading to IIA string.

Duality symmetry $ ext{SL}(2, ext{Z})$ acts on the tachyon and moduli.

Hints that tachyon fields relate to holonomy of flat $SU(2)$ gauge fields.

Abstract

We propose an exotic geometric M-theory dual for the weak coupling Type 0A string: compactification on a sub-Planckian $S^1\vee S^1$ (two circles connected at a point), where strong quantum effects lead to fields living on distinct resolutions of that space. Moreover we argue that tachyon condensation of the 0A theory corresponds to shrinking of one of the two circles leading to the IIA supersymmetric string. We use this and other dualities to provide an F-theoretic description of the axio-dilaton and the tachyonic field of Type 0B and argue for the existence of a strong coupling critical point of the potential using the resulting duality symmetry $\Gamma_0(2)\subset SL(2,\mathbb{Z})$ when tachyon field vanishes. The existence of this critical point can also be argued using conventional M-theory dualities. If this critical point is unique it is an unstable dS vacuum. Using this we propose a strong coupling conformal fixed point for a non-supersymmetric gauge theory in four dimensions living on coincident $D3^+-D3^-$branes of 0B. More generally we conjecture that the tachyon field can be identified with a pair of points on the torus parameterized by $z$ leading to the full duality group $SL(2,\mathbb{Z})$ acting on $(z,\tau)$. We find tantalizing hints that for both 0A and 0B the tachyon fields can be identified with the holonomy of a flat $SU(2)$ gauge field suggesting that we have two copies of the universe interacting with one another as if they are D-branes!