Abstract
We present a new exact treatment of Toverline{T} deformed 2D CFT in terms of the worldsheet theory of a non-critical string. The transverse dimensions of the non-critical string are represented by the undeformed CFT, while the two longitudinal light-cone di- rections are described by two scalar fields X+ and X− with free field OPE’s but with a modified stress tensor, arranged so that the total central charge adds up to 26. The relation between our X± field variables and 2D dilaton gravity is indicated. We compute the physical spectrum and the partition function and find a match with known results. We describe how to compute general correlation functions and present an integral expression for the three point function, which can be viewed as an exact formula for the OPE coefficients of the Toverline{T} deformed theory. We comment on the relationship with other proposed definitions of local operators.
Highlights
The transverse dimensions of the non-critical string are represented by the undeformed CFT, while the two longitudinal light-cone directions are described by two scalar fields X+ and X− with free field OPE’s but with a modified stress tensor, arranged so that the total central charge adds up to 26
Since the scalar fields and reparametrization ghosts are described by free field theory, our non-critical string formulation amounts to an exact non-perturbative solution of the T Tdeformed theory: the deformed amplitudes are obtained in a computable way from the correlation functions of the undeformed CFT
In recent work [26], Cardy studied the μ dependence of correlation functions of local operators in the T Tdeformed theory and showed that this dependence can be captured by a flow equation, expressed in terms of line integrals of energy momentum tensors
Summary
We introduce the non-critical string world-sheet theory and establish its equivalence with the T Tdeformed CFT at arbitrary central charge. This temporal gauge condition identifies the worldsheet coordinates with the chiral halves of the target space light-cone fields: X+(x+, x−) = x+ + X +(x−) and X−(x+, x−) = x− + X −(x+). Equations (2.6) provide the on-shell quantum definition of the light-cone coordinates The fact that they are expressed in terms of the stress tensor indicates that the space-time geometry is dynamical, and that left- and right-moving modes of the CFT are influencing each others trajectory via a geometric shockwave interaction. This periodicity condition implies that the temporal gauge formulation of the non-critical string theory leads to a non-trivial interaction between the left- and right-moving sectors: every time a right mover passes through a left mover, it gets shifted by an amount proportional to the light-cone momentum of the other particle. More detailed evidence in support of the equivalence will be given below
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