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Register a new userSuperconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
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For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data.
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We consider a family of $mathcal{N}=2$ superconformal field theories in four dimensions, defined as $mathbb{Z}_q$ orbifolds of $mathcal{N}=4$ Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $mathcal{N}=1$ superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of $N$, exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $mathcal{N}=4$ only at high orders in perturbation theory.
We complete the program of 2012.15792 about perturbative approaches for $mathcal{N}=2$ superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the possible ways among the vector multiplets of the quiver. Finally, we identify twisted and untwisted observables which probe the orbifold of $AdS_5times S^5$ with the aim of testing possible holographic perspectives of quiver theories in $mathcal{N}=2$.
General 1-point toric blocks in all sectors of N=1 superconformal field theories are analyzed. The recurrence relations for blocks coefficients are derived by calculating their residues and large $Delta$ asymptotics.
Massless flows between the coset model su(2)_{k+1} otimes su(2)_k /su(2)_{2k+1} and the minimal model M_{k+2} are studied from the viewpoint of form factors. These flows include in particular the flow between the Tricritical Ising model and the Ising model. Form factors of the trace operator with an arbitrary number of particles are constructed, and numerical checks on the central charge are performed with four particles contribution. Large discrepancies with respect to the exact results are observed in most cases.
Massless flows from the coset model su(2)_k+1 otimes su(2)_k /su(2)_2k+1 to the minimal model M_k+2 are studied from the viewpoint of form factors. These flows include in particular the flow from the Tricritical Ising model to the Ising model. By analogy with the magnetization operator in the flow TIM -> IM, we construct all form factors of an operator that flows to Phi_1,2 in the IR. We make a numerical estimation of the difference of conformal weights between the UV and the IR thanks to the Delta-sum rule; the results are consistent with the conformal weight of the operator Phi_2,2 in the UV. By analogy with the energy operator in the flow TIM -> IM, we construct all form factors of an operator that flows to Phi_2,1. We propose to identify the operator in the UV with sigma_1Phi_1,2.
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