Conveners
Formal SUSY Theories
- Masahito Yamazaki (University of Tokyo)
Formal SUSY Theories
- Masahito Yamazaki (University of Tokyo)
Formal SUSY Theories
- Masahito Yamazaki (University of Tokyo)
Formal SUSY Theories
- Wenbin Yan (Yau Mathematical Sciences Center, Tsinghua University)
Formal SUSY Theories
- Dan Xie
Formal SUSY Theories
- Wenbin Yan (Yau Mathematical Sciences Center, Tsinghua University)
Formal SUSY Theories
- Dan Xie
Formal SUSY Theories
- Dan Xie
The Nelson-Seiberg theorem and its extension relate supersymmetry breaking and R-symmetries in Wess-Zumino models, and found applications in phenomenology model building. We show that there are counterexample models with generic superpotential coefficients and non-generic R-charge assignment for fields. These models have more R-charge 2 fields than R-charge 0 fields, but give SUSY vacua with...
We study real higher-order constraints for ${\cal N}=1$ and ${\cal N}=2$ chiral superfields, which describe spontaneously broken (to ${\cal N}=0$) and non-linearly realized supersymmetry in the presence of a light axion of a spontaneously broken global $U(1)$. For ${\cal N}=1$ the constraint is of third order, while for ${\cal N}=2$ it is of fifth order and can be imposed on abelian vector or...
I will discuss various aspects of supersymmetric systems from the point of view of the theory of computational complexity. These include the claim that computing the Witten index of N=2 quantum mechanics is #P-complete and thus intractable. I will also discuss the complexity of finding supersymmetric ground states of local SUSY Hamiltonians and its implications for the problem of computing...
We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a...
Computing Donaldson-Thomas partition function of a G2 manifold has been a long standing problem. The key step for the problem is to understand the G2 instanton moduli space. I will discuss a string theory way to study the G2 instanton moduli space and explain how to compute the instanton partition function for a certain G2 manifold. An important insight comes from the twisted M-theory on the...
Pure spinor superfields provide a clean and powerful way of constructing and understanding supermultiplets, in any dimension and with any amount of supersymmetry, by using the algebraic geometry of the variety of square-zero elements in the corresponding supersymmetry algebra. This variety also classifies the possible twists of a supermultiplet. As such, it is natural to try and compute twists...
We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of G2 × SU(2) holonomy. Our derivation starts with an explicit description of the Batalin-Vilkovisky complex associated to the three-form multiplet in the pure spinor superfield formalism. We then determine the L∞ module structure of the supersymmetry algebra on the...
In this talk I explain how the maximal twist of eleven-dimensional supergravity in the free perturbative limit can be computed directly in the BV formalism. The maximal twist exists on manifolds of $G_2 \times SU(2)$ holonomy and is partially topological. After a short introduction to the BV formalism and twisting, I describe the $L_\infty$ action of the supersymmetry algebra on the component...
We study a set of four-dimensional N=2 superconformal field theories (SCFTs) labeled by a pair of simply-laced Lie groups. For some special choices, the resulting theories have identical central charges (a=c) without taking any large N limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of N=4 super Yang-Mills theory upon rescaling fugacities.
I will describe a method for computing confinement in $4d$ $\mathcal{N}=1$ theories that can be obtained by deforming $4d$ $\mathcal{N}=2$ of Class S. Such theories generically do not admit a conventional Lagrangian description. The confinement for this class of $4d$ $\mathcal{N}=1$ theories can be captured in topological properties of a complex curve, known as $\mathcal{N}=1$ curve, which can...
Localization method together with ADHM construction provide a powerful way to compute the exact partition function of 8 SUSY gauge theories. In particular, Nekrasov's partition function is interesting because of the non-perturbative corrections from instantons. It is, however, known to be difficult to perform the integrals in an analytic way that appear in the computation of instanton...
We study the elliptic genera of twisted 6d $(1,0)$ SCFTs from several approaches: 2d localization, modular bootstrape, Higgsing and twisted elliptic blowup equations. The twist is made when the 6d gauge algebra has outer automorphism symmetry. Upon twisted circle compactification, nontrivial 5d Kaluza-Klein theories appear. We provide a universal method to compute the twisted elliptic genera...
The study of the strong coupling behavior of quantum field theory is very challenging, with theories exhibiting interesting and mysterious strong coupling phenomena like dualities and symmetry enhancement. The tool of dimensional reduction, where the theories are realized through the compactification of a higher dimensional theory, can be used to give an organizing principle for these...
5d SCFTs can be constructed from M-theory on canonical threefold singularities. The Coulomb and Higgs branch information of the SCFT are encoded in the resolution and deformation of the singularity, respectively. I'm going to present the recent progress on isolated hypersurface singularities and non-isolated singularities.
I will describe my work arXiv:2106.11611 with Elli Pomoni and Wenbin Yan. We introduce and study tetrahedron instantons, which can be realized in string theory by D1-branes probing a configuration of intersecting D7-branes in flat spacetime with a nonzero constant background B-field. Physically they capture instantons on C^3 in the presence of the most general intersecting codimention-two...
The term S-folds denotes F-theory compactifications which involve non-trivial S-duality transformations. In this talk I will discuss 4d N=2 preserving S-folds and the worldvolume theories on D3-branes probing them. They consist of two new infinite series of superconformal theories whose distinction lies in the discrete torsion carried by the S-fold and in the difference in the asymptotic...
We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT$_\pm [\mathcal{T}_{\rm rank \;0}]$, to a (2+1)D interacting $\mathcal{N}=4$ superconformal field theory (SCFT) $\mathcal{T}_{\rm rank \;0}$ of rank 0, i.e.\ having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular...
I will present a systematic field theory prescription for constructing 3D N=4 mirror pairs involving quiver gauge theories beyond the well-known ADE examples. The construction involves a certain generalization of the S operation, which arises in the context of the 3d SL(2,Z) action on a CFT with a U(1) 0-form symmetry. I will show how this construction can be used to find Lagrangian...
Flavored Schur indices of 4d N=4 SCFTs encode many crucial information of the associated VOAs. For Lagrangian theories, the indices can be written as a multi-contour-integral of one-loop factor Z. In this talk, we will show that for 4d N=4 theories, some special residues of Z coincide with the free field characters of the bcβγ systems, proposed by Bonetti, Meneghelli and Rastelli, that realize...
In this talk, we investigate relationships between two families of $\mathcal W$-algebras, that is, the subregular $\mathcal W$-algebra for $\mathfrak{sl}_{n}$ and the principal $\mathcal{W}$-superalgebra for $\mathfrak{sl}_{1|n}$ in terms of their algebraic structure and representation theory.
The very beginning case is the Kazama-Suzuki coset construction of $\mathcal{N}=2$ superconformal...
I will describe a framework for computing the BPS spectrum of M-theory on a local Calabi-Yau threefold times R4xS1. Exponential Networks define counts of special Lagrangians in the mirror Calabi-Yau, thereby leading to a proposal for computing related DT invariants from geometric data of mirror curves. I will briefly sketch a connection to BPS quivers and a computation of the...
We introduce a class of new algebras, the shifted quiver Yangians, as the BPS algebras for type IIA string theory on general toric Calabi-Yau three-folds. We construct representations of the shifted quiver Yangian from general subcrystals of the canonical crystal. We derive our results via equivariant localization for supersymmetric quiver quantum mechanics for various framed quivers, where...
I will describe interplay between the study of supersymmetric line defects and the construction of link invariants. As an example, a certain UV-IR map for line defects in 4d N=2 theories of class-S motivates a new link "invariant" (with wall-crossing behaviors) for links in three-manifolds taking the form of a surface times a real line. This new link "invariant" gives a refined counting of the...
Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions ("adjoint QCD") flows to a phase with confinement and chiral symmetry breaking. In this talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of a renormalization group flow descending from SU(N) Seiberg-Witten theory, deformed by...
