Expanding 3d $$ \mathcal{N} $$ = 2 theories around the round sphere

We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a $$ \mathcal{N} $$ N = 2 large N Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large N spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.

Section: Jhep11(2021)211supporting

confidence: 65%

A 3d disordered superconformal fixed point

Chang

Colin-Ellerin

Peng

et al. 2021

“…The second derivative of Re F (t) at t SC also turns out to have an interesting meaning, and in fact encodes the central charge C defined in (B.8). More explicitly, it is given by [87] (see also [88])…”

Section: Jhep09(2021)149mentioning

confidence: 99%

Compactifying 5d superconformal field theories to 3d

Sacchi

Sela

Zafrir

2021

Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d$$ \mathcal{N} $$ N = 1 theories, we initiate a systematic study of compactifications of 5d$$ \mathcal{N} $$ N = 1 SCFTs on Riemann surfaces to 3d$$ \mathcal{N} $$ N = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $$ {E}_{N_f+1} $$ E N f + 1 SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.

“…Here ψ is a special function called the quantum dilogarithm, for which readers are referred to appendix D. The partition function in the limit b → 1 was studied in [50] and one can check that…”

Section: Jhep08(2021)158mentioning

confidence: 99%

“…The factor |Weyl(G)| is multiplied since that many saddle points, which all give the same perturbative expansion, collapse into a single Bethe-vacuum after the Weyl quotient. The perturbative expansion can be formally computed by performing Gaussian integrals [50,82]. For example,…”

Section: Jhep08(2021)158mentioning

confidence: 99%

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

Gang

Kim

Lee

et al. 2021

Self Cite

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.