Conformal boundary states for free bosons and fermions

TL;DR

This paper constructs a new family of conformal boundary states for free bosons and fermions, expanding the understanding of D-branes and boundary conditions in conformal field theories with potential applications in string theory.

Contribution

It introduces a novel family of boundary states that are fundamental and conformally invariant, generalizing known branes and satisfying key consistency conditions.

Findings

Boundary states satisfy Cardy's condition.

Boundary states account for all fundamental conformal D-branes.

Generalization to N=1 supersymmetry interpolates between BPS and non-BPS states.

Abstract

A family of conformal boundary states for a free boson on a circle is constructed. The family contains superpositions of conventional U(1)-preserving Neumann and Dirichlet branes, but for general parameter values the boundary states are fundamental and preserve only the conformal symmetry. The relative overlaps satisfy Cardy's condition, and each boundary state obeys the factorisation constraint. It is also argued that, together with the conventional Neumann and Dirichlet branes, these boundary states already account for all fundamental conformal D-branes of the free boson theory. The results can be generalised to the situation with N=1 world-sheet supersymmetry, for which the family of boundary states interpolates between superpositions of non-BPS branes and combinations of conventional brane anti-brane pairs.