Holography and the Coleman-Mermin-Wagner theorem

TL;DR

This paper explores how quantum fluctuations in holographic models prevent spontaneous symmetry breaking in certain curved spacetimes, aligning with the Coleman-Mermin-Wagner theorem, and reveals the emergence of algebraic long-range order at low temperatures.

Contribution

It demonstrates through one-loop calculations that bulk quantum fluctuations eliminate classical order parameters in holographic superconductors, extending the Coleman-Mermin-Wagner theorem to holographic duals.

Findings

Quantum fluctuations wash out the classical order parameter.

Low temperature phase exhibits algebraic long-range order.

Holography indicates IR quantum fluctuations are significant in AdS spacetimes.

Abstract

In 2+1 dimensions at finite temperature, spontaneous symmetry breaking of global symmetries is precluded by large thermal fluctuations of the order parameter. The holographic correspondence implies that analogous effects must also occur in 3+1 dimensional theories with gauged symmetries in certain curved spacetimes with horizon. By performing a one loop computation in the background of a holographic superconductor, we show that bulk quantum fluctuations wash out the classical order parameter at sufficiently large distance scales. The low temperature phase is seen to exhibit algebraic long range order. Beyond the specific example we study, holography suggests that IR singular quantum fluctuations of the fields and geometry will play an interesting role for many 3+1 dimensional asymptotically AdS spacetimes with planar horizon.