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Register a new userA study of N =1 SCFT derived from N =2 SCFT: index and chiral ring
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One can derive a large class of new $mathcal{N}=1$ SCFTs by turning on $mathcal{N}=1$ preserving deformations for $mathcal{N}=2$ Argyres-Dougals theories. In this work, we use $mathcal{N}=2$ superconformal indices to get indices of $mathcal{N}=1$ SCFTs, then use these indices to derive chiral rings of $mathcal{N}=1$ SCFTs. For a large class of $mathcal{N}=2$ theories, we find that the IR theory contains only free chirals if we deform the parent $mathcal{N}=2$ theory using the Coulomb branch operator with smallest scaling dimension. Our results provide interesting lessons on studies of $mathcal{N}=1$ theories, such as $a$-maximization, accidental symmetries, chiral ring, etc.
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We propose that a certain $4d$ $mathcal{N}=1$ $SU(2)times SU(2)$ gauge theory flows in the IR to an $mathcal{N}=3$ SCFT plus a single free chiral field. The specific $mathcal{N}=3$ SCFT has rank $1$ and a dimension three Coulomb branch operator. The flow is generically expected to land at the $mathcal{N}=3$ SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from $mathcal{N}=3$ superconformal symmetry, and use these to test our proposal. Finally, we discuss a generalization to another $mathcal{N}=1$ model that we propose is related to a certain rank $3$ $mathcal{N}=3$ SCFT through the turning of certain marginal deformations.
We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group. These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.
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 $lambda_{epsilonepsilonepsilon}/lambda_{sigmasigmaepsilon} = tan(1)$.
We build a bridge between two algebraic structures in SCFT: a VOA in the Schur sector of 4d $mathcal{N}=2$ theories and an associative algebra in the Higgs sector of 3d $mathcal{N}=4$. The natural setting is a 4d $mathcal{N}=2$ SCFT placed on $S^3times S^1$: by sending the radius of $S^1$ to zero, we recover the 3d $mathcal{N}=4$ theory, and the corresponding VOA on the torus degenerates to the associative algebra on the circle. We prove that: 1) the Higgs branch operators remain in the cohomology; 2) all the Schur operators of the non-Higgs type are lifted by line operators wrapped on the $S^1$; 3) no new cohomology classes are added. We show that the algebra in 3d is given by the quotient $mathcal{A}_H = {rm Zhu}_{s}(V)/N$, where ${rm Zhu}_{s}(V)$ is the non-commutative Zhu algebra of the VOA $V$ (for ${s}in{rm Aut}(V)$), and $N$ is a certain ideal. This ideal is the null space of the (${s}$-twisted) trace map $T_{s}: {rm Zhu}_{s}(V) to mathbb{C}$ determined by the torus 1-point function in the high temperature (or small complex structure) limit. It therefore equips $mathcal{A}_H$ with a non-degenerate (twisted) trace, leading to a short star-product according to the recent results of Etingof and Stryker. The map $T_{s}$ is easy to determine for unitary VOAs, but has a much subtler structure for non-unitary and non-$C_2$-cofinite VOAs of our interest. We comment on relation to the Beem-Rastelli conjecture on the Higgs branch and the associated variety. A companion paper will explore further details, examples, and some applications of these ideas.
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