On conformal invariance of interacting fields

We study the action of the conformal algebra on interacting fields. On a certain set of states the algebra is integrated to projective representations ofSU(2,2). These representations are shown to be equivalent to the representations of the interpolated discrete series ofSU(2,2). Using this result we give a formula for the two-point Wightman function for arbitrary spin and dimension of the field. Finally we discuss the limit when the dimension tends to the canonical value.     

Holographic dual of a boundary conformal field theory

We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e., boundary conformal field theory (BCFT). Our new holography, which may be called anti-de?Sitter BCFT, successfully calculates the boundary entropy or g function in two-dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g theorem. We also analyze the holographic dual of an interval at finite temperature and show that there is a first order phase transition.     

Holographic storage in sensitized polymethyl methacrylate blocks

The storage properties of thick PMMA-blocks, sensitized for =514 nm and containing residual monomer, are investigated by making use of holographic methods. The fundamental refractive index grating amplitude shows a characteristic development in a two-beam holographic experiment. A remarkable self-development of the light induced refractive index change is observed just as considerable higher harmonic amplitudes (strong nonlinear response). The recording-sensitivity is small in comparison to that of other storage materials and adversely affected by appreciable holographic scattering. The behavior of the samples during long storage times is investigated and the possibility of thermal fixing and superposition of holograms is shown. The interpretation of the observed properties and the behavior in the holographic experiments suggests a model of the microscopic processes: storage is essentially performed by light induced polymerisation of residual monomer.     

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.     

Check of AGT relation for conformal blocks on sphere

The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs. The diagram technique which arises in conformal block calculation involves propagators and vertices. We evaluated vertices with two Virasoro algebra descendants and explicitly checked the AGT relation up to the third order of the expansion for the 5-point and 6-point conformal blocks on sphere confirming all the predictions of arXiv:0906.3219 relevant in this situation. We propose that U(1)$U(1)$-factor can be extracted from the matrix elements of the free field vertex operators. We studied the n-point case, and found out that our results confirm the AGT conjecture up to the third order expansions.     

Orbifold conformal blocks and the stack of pointed G-covers

Starting with a vertex algebra V, a finite group G of automorphisms of V, and a suitable collection of twisted V-modules, we construct (twisted) D-modules on the stack of pointed G-covers, introduced by Jarvis, Kaufmann, and Kimura. The fibers of these sheaves are spaces of orbifold conformal blocks defined in joint work with Edward Frenkel. The key ingredient is a G-equivariant version of the Virasoro uniformization theorem.