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We show that the three different looking BPS partition functions, namely the elliptic genus of the 6d $mathcal{N}=(1,0)$ $Sp(1)$ gauge theory with $10$ flavors and a tensor multiplet, the Nekrasov partition function of the 5d $mathcal{N}=1$ $Sp(2)$ gauge theory with $10$ flavors, and the Nekrasov partition function of the 5d $mathcal{N}=1$ $SU(3)$ gauge theory with $10$ flavors, are all equal to each other under specific maps among gauge theory parameters. This result strongly suggests that the three gauge theories have an identical UV fixed point. Type IIB 5-brane web diagrams play an essential role to compute the $SU(3)$ Nekrasov partition function as well as establishing the maps.
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We propose new five-dimensional gauge theory descriptions of six-dimensional $mathcal{N}=(1,0)$ superconformal field theories arising from type IIA brane configurations including an $ON^0$-plane. The new five-dimensional gauge theories may have $SO$, $Sp$, and $SU$ gauge groups and further broaden the landscape of ultraviolet complete five-dimensional $mathcal{N}=1$ supersymmetric gauge theories. When we include an $O8^-$-plane in addition to an $ON^0$-plane, T-duality yields two $O7^-$-planes at the intersections of an $ON^0$-plane and two $O5^0$-planes. We propose a novel resolution of the $O7^-$-plane with four D7-branes in such a configuration, which enables us to obtain three different types of five-dimensional gauge theories, depending on whether we resolve either none or one or two $O7^-$-planes. Such different possibilities yield a new five-dimensional duality between a D-type $SU$ quiver and an $SO-Sp$ quiver theories. We also claim that a twisted circle compactification of a six-dimensional superconformal field theory may lead to a five-dimensional gauge theory different from those obtained by a simple circle compactification.
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We explore the superstring theory on AdS_3 x S^3 x T^4 in the framework given in hep-th/9806194. We argue on the Hilbert space of space-time CFT, and especially construct a suitable vacuum of this CFT from the physical degrees of freedom of the superstring theory in bulk. We first construct it explicitly in the case of p=1, and then present a proposal for the general cases of p>1. After giving some completion of the GKSs constructions of the higher mode operators (in particular, of those including spin fields), we also make some comparison between the space-time CFT and T^{4kp}/S_{kp} SCFT, namely, with respect to the physical spectrum of chiral primaries and some algebraic structures of bosonic and fermionic oscillators in both theories. We also observe how our proposal about the Hilbert space of space-time CFT leads to a satisfactory correspondence between the spectrum of chiral primaries of both theories in the cases of p>1.
We study the conformal bootstrap constraints for 3D conformal field theories with a $mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $epsilon$ that is invariant under the symmetry. When there is additionally a single relevant odd scalar $sigma$, we map out the allowed space of dimensions and three-point couplings of such Ising-like CFTs. If we allow a second relevant odd scalar $sigma$, we identify a feature in the allowed space compatible with 3D $mathcal{N}=1$ superconformal symmetry and conjecture that it corresponds to the minimal $mathcal{N}=1$ supersymmetric extension of the Ising CFT. This model has appeared in previous numerical bootstrap studies, as well as in proposals for emergent supersymmetry on the boundaries of topological phases of matter. Adding further constraints from 3D $mathcal{N}=1$ superconformal symmetry, we isolate this theory and use the numerical bootstrap to compute the leading scaling dimensions $Delta_{sigma} = Delta_{epsilon} - 1 = .58444(22)$ and three-point couplings $lambda_{sigmasigmaepsilon} = 1.0721(2)$ and $lambda_{epsilonepsilonepsilon} = 1.67(1)$. We additionally place bounds on the central charge and use the extremal functional method to estimate the dimensions of the next several operators in the spectrum. Based on our results we observe the possible exact relation $lambda_{epsilonepsilonepsilon}/lambda_{sigmasigmaepsilon} = tan(1)$.
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