Abstract
We describe the effect of the marginal deformation of the mathcal{N} = (4, 4) super-conformal (T4)N/SN orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-N approximation. Our analysis of their dynamics explores the explicit analytic form of the genus-zero four-point function involving two R-neutral Ramond fields and two deformation operators. We compute this correlation function with two different approaches: the Lunin-Mathur path-integral technique and the stress-tensor method. From its short distance limits, we extract the OPE structure constants and the scaling dimensions of non-BPS fields appearing in the fusion. In the deformed CFT, at second order in the deformation parameter, the two-point function of the n-twisted Ramond fields is UV-divergent. We perform an appropriate regularization, together with a renormalization of the undeformed fields, obtaining finite, well-defined corrections to their two-point functions and their bare conformal weights, for n < N. The fields with maximal twist n = N remain protected from renormalization, with vanishing anomalous dimensions.
Highlights
Where λ is a dimensionless coupling constant and O[(2in] t)(z, z) a scalar modulus marginal operator with twist 2
We describe the effect of the marginal deformation of the N = (4, 4) superconformal (T 4)N /SN orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-N approximation
Spin fields have the responsibility of creating the anti-periodic boundary conditions of fermions in the Ramond sector of a CFT defined on the complex plane
Summary
Each copy contains four free scalar bosons XIi(z, z), and four free fermions ψIi (z), where i = 1, . N the copies; the total central charge with the 4N bosons and 4N fermions is corb = 6N. The holomorphic N = 4 super-conformal symmetry is generated by the stress-energy tensor T (z), the SU(2) R-currents Jr(z), r = 1, 2, 3, and the super-currents Ga(z), Ga(z), which can be expressed in terms of the free fields as. The anti-chiral currents, T(z), J3(z), Ga(z), Gˆa(z), have analogous forms in terms of the right-moving fields. For each CFT copy, the four bosons XIi(z, z) are coordinates on the torus T 4 and, the periodic identifications break the rotational symmetry of four-dimensional. SU(2) acts on both sectors, so the corresponding fermionic charges are the eigenvalues of the “total” conserved current J(z)+J(z).
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