We explore the n-twisted Ramond sector of the deformed two-dimensional $$ \mathcal{N} $$ N = (4, 4) superconformal (T4)N/SN orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-N limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-N limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.

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We examine the behavior of the Ramond ground states in the D1-D5 CFT after a deformation of the free-orbifold sigma model on target space ($$ {\mathbbm{T}}^4 $$ T 4 )N/SN by a marginal interaction operator. These states are compositions of Ramond ground states of the twisted and untwisted sectors. They are characterized by a conjugacy class of SN and by the set of their “spins”, including both R-charge and “internal” SU(2) charge. We compute the four-point functions of an arbitrary Ramond ground state with its conjugate and two interaction operators, for genus-zero covering surfaces representing the leading orders in the large-N expansion. We examine short distance limits of these four-point functions, shedding light on the dynamics of the interacting theory. We find the OPEs and a collection of structure constants of the ground states with the interaction operators and a set of resulting non-BPS twisted operators. We also calculate the integrals of the four-point functions over the positions of the interaction operators and show that they vanish. This provides an explicit demonstration that the Ramond ground states remain protected against deformations away of the free orbifold point, as expected from algebraic considerations using the spectral flow of the $$ \mathcal{N} $$ N = (4, 4) superconformal algebra with central charge c = 6N.

We implement a conformal time scale factor duality for Friedmann-RobertsonWalker cosmological models, which is consistent with the weak energy condition. The requirement for self-duality determines the equations of state for a broad class of barotropic fluids. We study the example of a universe filled with two interacting fluids, presenting an accelerated and a decelerated period, with manifest UV/IR duality. The associated self-dual scalar field interaction turns out to coincide with the "radiation-like" modified Chaplygin gas models. We present an equivalent realization of them as gauged Kähler sigma models (minimally coupled to gravity) with very specific and interrelated Kähler-and super-potentials. Their applications in the description of hilltop inflation and also as quintessence models for the late universe are discussed.