We propose an $$ \mathcal{N}=2 $$ preserving deformation that leads to the confining phase of the 3d reduction of the $\textit{D}$ [SU($\textit{N}$)] Argyres-Douglas theories, referred to as 𝔻 [SU($\textit{N}$)]. This deformation incorporates monopole superpotential terms, which have recently played interesting roles in exploring possible RG fixed points of 3d supersymmetric gauge theories. Employing this confining phenomenon in 3d 𝔻 [SU($\textit{N}$)] theories, we also propose a deconfined version of the Kim-Park duality, an IR duality for 3d $$ \mathcal{N}=2 $$ adjoint SQCDs, where an adjoint matter field is replaced by a linear quiver tail of 𝔻 [SU($\textit{N}$)]. Surprisingly, both the confinement of deformed 𝔻 [SU($\textit{N}$)] and the deconfined Kim-Park duality can be proven only assuming some basic 3d $$ \mathcal{N}=2 $$ IR dualities. Finally, we propose a variant of the Kim-Park duality deformed by a single monopole superpotential term, which can also be derived using the same method.

China

Chiung Hwang

South Korea

Sungjoon Kim

S-confinement of 3d Argyres-Douglas theories and the Seiberg-like duality with an adjoint matter

We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing N M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on S 2 × ℝ. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the N 2 degrees of freedom except   <math> <msup> <mi>N</mi> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msup> </math>  $$ {N}^{\frac{3}{2}} $$  of them, even in the high temperature deconfined phase. The resulting large N free energy statistically accounts for the Bekenstein-Hawking entropy of large BPS black holes in AdS4 × S 7. Our Cardy free energy also suggests a finite N version of the   <math> <msup> <mi>N</mi> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msup> </math>  $$ {N}^{\frac{3}{2}} $$  degrees of freedom.

Sunjin Choi

Italy

Seok Kim

Quantum vortices, M2-branes and black holes

We continue our analysis of bad theories initiated in [1], focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver.

Simone Giacomelli

United Kingdom

Fabio Marino

Sara Pasquetti

Matteo Sacchi

Probing bad theories with the dualization algorithm. Part II.

In Special Geometry there are two inequivalent notions of “Kodaira type” for a singular fiber: one associated with its local monodromy and one with its Hwang-Oguiso characteristic cycle. When the two Kodaira types are not equal the geometry is subtler and its deformation space gets smaller (“partially frozen” singularities). The paper analyzes the physical interpretation of the Hwang-Oguiso invariant in the context of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 QFT and describes the surprising phenomena which appear when it does not coincide with the monodromy type. The Hwang-Oguiso multiple fibers are in one-to-one correspondence with the partially frozen singularities in M-theory compactified on a local elliptic K3: a chain of string dualities relates the two geometric set-ups. Paying attention to a few subtleties, this correspondence explains in purely geometric terms how the “same” Kodaira elliptic fiber may have different deformations spaces. The geometric computation of the number of deformations agrees with the physical expectations. At the end we briefly outline the implications of the Hwang-Oguiso invariants for the classification program of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 SCFTs.

Sergio Cecotti

Hwang-Oguiso invariants and frozen singularities in special geometry

Recently an algorithm to build SL(2, ℤ) duals, including mirror duals, of 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 quiver theories and their 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with U(N  c ) gauge group in 3d and USp(2N  c ) in 4d, while in an upcoming paper we will consider linear quivers which, in the 3d case, have both unitary and special unitary bad nodes.

Probing bad theories with the dualization algorithm. Part I

Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 linear quivers and for their 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the 3d theories, where mirror symmetry is realized as S-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of S-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is SL(2, ℤ) in 3d and PSL(2, ℤ) in 4d. This also produces dualities for 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 theories with Chern-Simons couplings, some of which have enhanced   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supersymmetry, and their new 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany-Witten move in field theory.

Riccardo Comi

The SL(2, ℤ) dualization algorithm at work

We propose new 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 Seiberg-like dualities by considering various monopole superpotential deformations on 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 U(N  c ) SQCDs with fundamental and adjoint matter fields. We provide nontrivial evidence of these new dualities by comparing the superconformal indices, from which we analyze the change of the moduli space due to the monopole deformation. In addition, we perform the F-maximization to check the relevance of the monopole deformation for some examples, one of which is found to exhibit nontrivial symmetry enhancement in the IR. We prove such enhancement of the global symmetry using the superconformal index.

Jaemo Park

Monopole deformations of 3d Seiberg-like dualities with adjoint matters

We introduce an algorithm to piecewise dualize linear quivers into their mirror dual. The algorithm uses two basic duality moves and the properties of the <math><mrow><mi>S</mi></mrow></math>-wall which can all be derived by iterative applications of Seiberg-like dualities.

Rethinking mirror symmetry as a local duality on fields

It is an interesting question whether a given infra-red duality between quantum field theories can be explained in terms of other more elementary dualities. For example recently it has been shown that mirror dualities can be obtained by iterative applications of Seiberg-like dualities. In this paper we continue this line of investigation focusing on theories with tensor matter. In such cases one can apply the idea of deconfinement, which consists of trading the tensor matter for extra gauge nodes by means of a suitable elementary duality. This gives an auxiliary dual frame which can then be manipulated with further dualizations, in an iterative procedure eventually yielding an interesting dual description of the original theory. The sequential deconfinement technique has avatars in different areas of mathematical physics, such as the study of hypergeometric and elliptic hypergeometric integral identities or of 2d free field correlators. We discuss various examples in the context 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric theories, which are related to elliptic hypergeometric integrals. These include a new self-duality involving a quiver theory which exhibits a non-trivial global symmetry enhancement to E 6.

Lea Bottini

Dualities from dualities: the sequential deconfinement technique

In this paper we present various 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 dualities involving theories obtained by gluing two E[USp(2N)] blocks via the gauging of a common USp(2N) symmetry with the addition of 2L fundamental matter chiral fields. For L = 0 in particular the theory has a quantum deformed moduli space with chiral symmetry breaking and its index takes the form of a delta-function. We interpret it as the Identity wall which identifies the two surviving USp(2N) of each E[USp(2N)] block. All the dualities are derived from iterative applications of the Intriligator-Pouliot duality. This plays for us the role of the fundamental duality, from which we derive all others. We then focus on the 3d version of our 4d dualities, which now involve the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 T[SU(N)] quiver theory that is known to correspond to the 3d S-wall. We show how these 3d dualities correspond to the relations S 2 = −1, S  −1 S = 1 and STS = T  −1 S  −1 T  −1 for the S and T generators of SL(2, ℤ). These observations lead us to conjecture that E[USp(2N)] can also be interpreted as a 4d S-wall.