On actions for (entangling) surfaces and DCFTs

TL;DR

This paper develops a new variational principle for entangling surfaces and interfaces, linking geometric response coefficients to physical properties, and applies it to conformal field theories with boundaries and defects.

Contribution

It introduces a comprehensive variational framework for surfaces and interfaces, capturing all diffeomorphism constraints and linking geometric tensors to physical response coefficients.

Findings

Derived a new variational principle for entangling surfaces.

Identified geometric parity-odd contributions to elastic properties.

Constrained stress tensor structures in conformal field theories with boundaries.

Abstract

The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by Carter, we introduce a new variational principle for (entangling) surfaces. This principle captures all diffeomorphism constraints on surface/interface actions and their associated spacetime stress tensor. The different couplings to the geometric tensors appearing in the surface action are interpreted in terms of response coefficients within elasticity theory. An example of a surface action with edges at the two-derivative level is studied, including both the parity-even and parity-odd sectors. Its conformally invariant counterpart restricts the type of conformal anomalies that can appear in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics, it is shown that classification methods can be used to constrain the stress tensor of (entangling) surfaces at a given order in derivatives. This analysis reveals a purely geometric parity-odd contribution to the Young modulus of a thin elastic membrane. Extending this novel variational principle to BCFTs and DCFTs in curved spacetimes allows to obtain the Ward identities for diffeomorphism and Weyl transformations. In this context, we provide a formal derivation of the contact terms in the stress tensor and of the displacement operator for a broad class of actions.