Triangle Seminars

Abstract:
A solvable irrelevant deformation of AdS3/CFT2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed by Kutasov et al. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable T\bar{T}-deformations of two-dimensional CFTs. Thought of as a worldsheet sigma-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV. In this talk, after giving an introduction to this class of solvable theories, I will present explicit results for their observables.

Abstract:
In two dimensional topological phases of matter, processes
depend on gross topology rather than detailed geometry. Thinking in 2+1
dimensions, particle world lines can be interpreted as knots or links,
and the amplitude for certain processes becomes a topological invariant
of that link. While sounding rather exotic, we believe that such phases
of matter not only exist, but have actually been observed in quantum
Hall experiments, and could provide a uniquely practical route to
building a quantum computer. Possibilities have also been proposed for
creating similar physics in systems ranging from superfluid helium to
strontium ruthenate to semiconductor-superconductor junctions to quantum
wires to spin systems to graphene to cold atoms.

Abstract:
Why do some systems organise themselves into well ordered patterns with astonishing symmetry and regularity, while other superficially similar systems produce defects and disorder? In systems where two different length scales are unstable, the nonlinear interaction between the different modes is key: steady complex patterns can be stabilised when the modes act together to reinforce each other. But, if the two types of pattern compete with each other, the outcome can be considerably more complicated: a time-dependent disordered mixture of patterns constantly shifting and changing. In a small domain, the nature of the interaction between a small number of modes on each length scale can readily be computed. In a large domain, each mode can interact with hundreds of other modes, but the overall behaviour still appears to be guided by small-domain considerations.

Abstract:
We will argue that superstring theory on \({\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4\) with the smallest amount of NS-NS flux (``\(k=1\)'') is dual to the spacetime CFT given by the large \(N\) limit of the free symmetric product orbifold \(\mathrm{Sym}^N(\mathbb{T}^4)\). The worldsheet theory, at \(k=1\), is defined using the hybrid formalism in which the \({\rm AdS}_3\times {\rm S}^3\) part is described by a \(\mathfrak{psu}(1,1|2)_1\) WZW model (which is well defined).
Unlike the case for \(k\geq 2\), it turns out that the string spectrum at \(k=1\) does not exhibit a long string continuum, and perfectly matches with the large \(N\) limit of the symmetric product. The fusion rules of the symmetric orbifold are also reproduced from the worldsheet perspective.

This proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory.