Abstract
We calculate the torus partition sum of a general CFT2 with left and right moving conserved currents J and overline{J} , perturbed by a combination of the irrelevant operators Toverline{T},Joverline{T} and Toverline{J} . We use string theory techniques to write it as an integral transform of the partition sum of the unperturbed CFT with chemical potentials for the left and right moving conserved charges. The resulting expression transforms in the right way under the modular group, and reproduces the known spectrum of these models. We also derive a formula for the partition function of deformed CFT2 with non-vanishing chemical potentials.
Highlights
We find that the partition sum (1.5) is given by
Comparing the second line of (4.6) to (A.14), we see that the path integral over y gives rise in this case to the partition sum Zinv(τ, τ, χ, χ) defined in (A.7), (A.11), (A.13)
We used a technique based on holography, that has been used before to determine the spectra of these theories
Summary
All partition sums in (3.2) are functions of the modulus of the worldsheet torus, (τ, τ ), and Zws needs to be integrated over all inequivalent values of the moduli. Expression (3.14) is related to the results of [8] It gives the partition sum of the deformed theory as a convolution of the undeformed partition sum with the kernel. (2) The partition sum of the deformed theory is obtained by smearing that of the undeformed theory over a region whose size grows as the coupling λ increases This is the way that the torus partition sum exhibits the√non-locality of the theory, and the fact that the non-locality scale is proportional to λ. The cancellation between the two terms on the r.h.s. of (3.23) is the cancellation mentioned above (around (3.8)) between the Nambu-Goto contribution to the energy and that of the (critical) B-field
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