Tensionless strings from worldsheet symmetries

Abstract

Abstract:We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.

Tensionless superstrings: view from the worldsheet

“…We saw in the bosonic case in [17], that when we considered closed tensionless strings with c M = 0, the residual gauge symmetry truncated to a single copy of the Virasoro algebra indicating a deep relation between the tensionless closed string and the open string, previously anticipated e.g. in [23].…”

“…This sends the worldsheet speed of light to zero. For details of this procedure, we encourage the interested reader to have a look at [14,17]. The apparent dichotomy between an ultra-relativistic limit and naming the residual symmetry the Galilean conformal symmetry is resolved when one understands that in the special case of two dimensions, the non-relativistic contraction ({σ → ǫσ, τ → τ with ǫ → 0}) and the above mentioned ultra-relativistic limit yields the same algebra from the two copies of the Virasoro algebra of the tensile string.…”

Inhomogeneous tensionless superstrings

“…A very natural generalisation of the analysis of [40] is to consider tensionless superstrings. This was done in [42], following the lead of [41], and in the next sections, we briefly review our previous construction.…”

“…But this remains one of our principal motivations behind attempting to realise (1.11) as a symmetry algebra. We shall, however, comment on a rather interesting distinction between the homogeneous and inhomogeneous cases later in the section where we investigate some old claims in the literature about the equivalence of closed and open strings in the tensionless theory building on our bosonic analysis in [40]. Apart from the above, and most importantly, as we will elaborate immediately, the inhomogeneous tensionless superstring is the general solution in the space of tensionless superstring theories, while the homogeneous one is a special case.…”

“…One of the interesting features of our bosonic analysis in [40] was that we could provide more hints to the claim that in the tensionless limit, closed strings behave like open strings [51]. We focused on the residual symmetry algebra of the tensionless bosonic string, which is the 2d GCA (1.9) and used the fact that when we are looking at theories where c M = 0, the 2d GCA truncates to a single copy of the Virasoro algebra.…”