Microcanonical Simulation of Complex Actions: The Wess Zumino Witten Case

TL;DR

This paper demonstrates the effectiveness of microcanonical simulation in analyzing the complex Wess Zumino Witten action, successfully identifying critical points and phase transitions on small lattices, with potential applications to D-branes.

Contribution

It introduces a microcanonical simulation method for complex actions and verifies its applicability on the Wess Zumino Witten model, revealing critical points and phase behavior.

Findings

Successfully identified two critical points of the Wess Zumino Witten action.

Demonstrated critical behavior on an 8x8 lattice.

Discussed extensions to D-brane studies.

Abstract

We present the main results of our microcanonical simulation of the Wess Zumino Witten action functional. This action, being highly non-trivial and capable of exhibiting many different phase transitions, is chosen to be representative of general complex actions. We verify the applicability of microcanonical simulation by successfully obtaining two of the many critical points of the Wess Zumino Witten action. The microcanonical algorithm has the additional advantage of exhibiting critical behaviour for a small $8\times 8$ lattice. We also briefly discuss the subtleties that, in general, arise in simulating a complex action. Our algorithm for complex actions can be extended to the study of D-branes in the Wess Zumino Witten action.