Negative-Tension Branes and Tensionless 1/2 Brane in Boundary Conformal Field Theory

TL;DR

This paper explores boundary conformal field theory with a large electromagnetic field on an unstable Dp-brane, identifying marginal deformations that produce tensionless and negative-tension branes, and constructing their boundary states.

Contribution

It provides exact marginal deformations in BCFT for a Dp-brane under specific electromagnetic conditions, revealing tensionless and negative-tension branes and constructing their boundary states.

Findings

Exponential deformation yields a tensionless half brane.

Hyperbolic sine and cosine deformations produce negative-tension branes.

Boundary states constructed via T-duality and BCFT methods.

Abstract

In the framework of boundary conformal field theory we consider a flat unstable D$p$-brane in the presence of a large constant electromagnetic field. Specifically, we study the case that the electromagnetic field satisfy the following three conditions: (i) a constant electric field is turned on along the $x^1$ direction ($E_{1}\ne 0$); (ii) the determinant of the matrix $(\eta + F)$ is negative so that it lies in the physical region ($-\det (\eta + F)>0$); (iii) the 11-component of its cofactor is positive to the large electromagnetic field. In this case, we identify exactly marginal deformations depending on the spatial coordinate $x^1$. They correspond to tachyon profiles of hyperbolic sine, exponential, and hyperbolic cosine types. Boundary states are constructed for these deformations by utilizing T-duality approach and also by directly solving the overlap conditions in BCFT. The exponential type deformation gives a tensionless half brane connecting the perturbative string vacuum and one of the true tachyon vacua, while the others have negative tensions. This is in agreement with the results obtained in other approaches.