NS5-branes on an ellipsis and novel marginal deformations with parafermions

Abstract

We consider NS5-branes distributed along the circumference of an ellipsis and explicitly construct the corresponding gravitational background. This provides a continuous line of deformations between the limiting cases, considered before, in which the ellipsis degenerates into a circle or into a bar. We show that a slight deformation of the background corresponding to a circle distribution into an ellipsoidal one is described by a novel non-factorizable marginal perturbation of bilinears of dressed parafermions. The latter are naturally defined for the circle case since, as it was shown in the past, the background corresponds to an orbifold of the exact conformal field theory coset model SU(2)/U(1) × SL(2, R)/U(1). We explore the possibility to define parafermionic objects at generic points of the ellipsoidal families of backgrounds away from the circle point. We also discuss a new limiting case in which the ellipsis degenerates into two infinitely stretched parallel bars and show that the background is related to the Eguchi-Hanson metric, via T-duality.

Holographic approach to deformations of NS5-brane distributions and exact CFTs

“…In the next section we will identify them with the N = 1 σ model deformations induced by changing the circular distribution of NS5-branes to an elliptical one. In particular, the first line above will be related to the deformation of the bosonic part, thus recovering the result in [17], the second line will correspond to the deformation of the fermion bilinears and the third line to the deformation of the quartic, in the fermions, term.…”

“…The vertex operators V sl j;m,m decompose as 17) where π j;m,m are primaries of the non-compact parafermion theory at level k+2, and Q L (z) and Q R (z) are the holomorphic and antiholomorphic parts of Q. The conformal dimensions of π j;m,m read:…”

“…Namely, either from the corresponding N = 1 supersymmetric σ model viewpoint or from the exact CFT approach of the previous section as an exactly marginal perturbation based on the holographic conjecture. First we consider the simpler case of the circular distribution deformed into a small ellipsis and complete the analysis of [17] which was performed only for the bosonic part of the supersymmetric action. Subsequently, we consider the general planar deformation.…”

“…Given a density distribution one can construct the corresponding supergravity solution from (2.1)-(2.3). In our case it is convenient to parameterize the Cartesian coordinates in a way appropriate to the density (4.1) as [17] x = ℓ 1 sinh ρ cos θ cos τ, sinh ρ cos θ sin τ, cosh ρ sin θ cos ψ, sinh…”

“…The leading order correction to (2.29), corresponding to an infinitesimal deformation of the circle towards an ellipsis and after the proper T-duality and a reparameterization, reads [17] (see eq. (38) in that ref.…”