RG flows and cascades of $Lif_4^{(2)}\times S^1\times S^5$ vacua

TL;DR

This paper studies Lifshitz vacua in string theory, showing how deformations lead to flows between different Lifshitz solutions with varying dynamical exponents, and explores their IR and UV behaviors including decoupling of massive modes.

Contribution

It introduces exact deformations of Lifshitz vacua supported by massive B-fields, revealing flows to supersymmetric massless B-field solutions and cascading Lifshitz phases with integral dynamical exponent jumps.

Findings

Massive B modes decouple in IR, leaving massless modes to dominate dynamics.

Deformations induce flows from Lif_4^{(2)} to Lif_4^{(3)} vacua, with supersymmetry emerging in IR.

Cascading Lifshitz vacua exhibit integral jumps in dynamical exponent along the flow.

Abstract

The (F1,D2,D8) brane configuration produces $Lif_4^{(2)}\times {S}^1\times S^5$ Lifshitz vacua supported by `massive' $B$-field. We present exact deformations of this system under which new massless $B$-modes of strings also get excited. Due to these massless modes the deformed solutions flow to conformally $Lif_4^{(3)}\times S^1\times S^5$ vacua in the IR. The latter types are supersymmetric solutions of ordinary type IIA theory. The massive and massless $B_{\mu\nu}$ modes segregate out in the IR. We confirm that the massive $B$ mode and cosmological constant indeed decouple from the theory rendering the IR field dynamics controlled by massless fields only. A similar effect is observed on the UV side of the flow where a relativistic regime reappears. We also present `cascading' Lifshitz vacua in which dynamical exponent has integral jumps along the flow, $Lif_4^{(3)}\to Lif_4^{(2)}\to Lif_4^{(1)}$. The critical $Lif_4^{(2)}$ theory separates `deconfining' $Lif_4^{(3)}$ IR theory from the confining Yang-Mills phase in UV.