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Register a new userOn the fermion-boson correspondence for correlation functions of disorder operators
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When a quantum field theory possesses topological excitations in a phase with spontaneously broken symmetry, these are created by operators which are non-local with respect to the order parameter. Due to non-locality, such disorder operators have non-trivial correlation functions even in free massive theories. In two dimensions, these correlators can be expressed exactly in terms of solutions of non-linear differential equations. The correlation functions of the one-parameter family of non-local operators in the free charged bosonic and fermionic models are the inverse of each other. We point out a simple derivation of this correspondence within the form factor approach
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The two-dimensional ghost systems with negative integral central charge received much attention in the last years for their role in a number of applications and in connection with logarithmic conformal field theory. We consider the free massive bosonic and fermionic ghost systems and concentrate on the non-trivial sectors containing the disorder operators. A unified analysis of the correlation functions of such operators can be performed for ghosts and ordinary complex bosons and fermions. It turns out that these correlators depend only on the statistics although the scaling dimensions of the disorder operators change when going from the ordinary to the ghost case. As known from the study of the ordinary case, the bosonic and fermionic correlation functions are the inverse of each other and are exactly expressible through the solution of a non-linear differential equation.
We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural, well-known deformations parametrized by a parameter Q: the former one is related to the deformed boson-fermion correspondence introduced by N. Jing, while the latter is the so-called Q-boson, arising also in the context of quantum groups. These deformations are equivalent and can be realized in the same way in the algebra of Hall-Littlewood symmetric functions. Without a deformation, these reduce to Schur functions, which can be used to construct a generating function of plane partitions, reproducing a topological string partition function on $C^3$. We show that a deformation of both systems leads then to a deformed generating function, which reproduces topological string partition function of the conifold, with the deformation parameter Q identified with the size of $P^1$. Similarly, a deformation of the fermion one-point function results in the A-brane partition function on the conifold.
We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible $mathcal{N} = 1$ multiplets and some cases of interest for $mathcal{N} = 2$. As an application of the formalism we prove that certain $mathcal{N} = 2$ spinning chiral operators (also known as exotic chiral primaries) do not admit a consistent three-point function with the stress tensor and therefore cannot be present in any local SCFT. This extends a previous proof in the literature which only applies to certain classes of theories. To each superdescendant we associate a superconformally covariant differential operator, which can then be applied to any correlator in superspace. In the case of three-point functions, we introduce a convenient representation of the differential operators that considerably simplifies their action. As a consequence it is possible to efficiently obtain the linear relations between the OPE coefficients of the operators in the same superconformal multiplet and in turn streamline the computation of superconformal blocks. We also introduce a Mathematica package to work with four dimensional superspace.
Using the idea of the quantum inverse scattering method, we introduce the operators $mathbf{B}(x), mathbf{C}(x)$ and $mathbf{tilde{B}}(x), mathbf{tilde{C}}(x)$ corresponding to the off-diagonal entries of the monodromy matrix $T$ for the phase model and $i$-boson model in terms of bc fermions and neutral fermions respectively, thus giving alternative treatment of the KP and BKP hierarchies. We also introduce analogous operators $mathbf{B}^{*}(x)$ and $mathbf{C}^{*}(x)$ for the charged free boson system and show that they are in complete analogy to those of $bc$ fermionic fields. It is proved that the correlation function $langle 0|mathbf{C}(x_N)cdotsmathbf{C}(x_1)mathbf{B}(y_1)cdots $ $mathbf{B}(y_N)|0rangle$ in the $bc$ fermionic fields is the inverse of the correlation function $langle 0|mathbf{C}^{*}(x_N)cdotsmathbf{C}^{*}(x_1)mathbf{B}^{*}(y_1)cdots mathbf{B}^{*}(y_N)|0rangle$ in the charged free bosons.
We consider operators in N=4 SYM theory which are dual, at strong coupling, to classical strings rotating in S^5. Three point correlation functions of such operators factorize into a universal contribution coming from the AdS part of the string sigma model and a state-dependent S^5 contribution. Consequently a similar factorization arises for the OPE coefficients. In this paper we evaluate the AdS universal factor of the OPE coefficients which is explicitly expressed just in terms of the anomalous dimensions of the three operators.
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