arXiv subjects

Mykola Dedushenko

Publications and source records attributed to Mykola Dedushenko.

At least 19 recordsLinked to original sources

arXiv2025

Coulomb Branches of Noncotangent Type: a Physics Perspective

We study the Coulomb-branch sector of 3D $\mathcal{N}=4$ gauge theories with half-hypermultiplets in general pseudoreal representations $\mathbf{R}$ ("noncotangent" theories). This yields (short) quantization of the Coulomb branch and correlators of the Coulomb branch operators captured by the 1d topological sector. This is done by extending the hemisphere partition function approach to noncotangent matter. In this setting one must first cancel the parity anomaly, and overcome an obstacle that $(2,2)$ boundary conditions for half-hypers are generically incompatible with gauge symmetry. Using the Dirichlet boundary conditions for the gauge fields and a careful treatment of half-hypermultiplet boundary data, we describe the resulting shift/difference operators implementing monopole insertions (including bubbling effects) on $HS^3$, and use the $HS^3$ partition function as a natural module on which the Coulomb-branch operator algebra $\mathcal{A}_C$ is represented. As applications we derive generators and relations of $\mathcal{A}_C$ for $SU(2)$ theories with general matter (including half-integer spin representations), analyze theories with Coulomb branch $y^2=z(x^2-1)$, compute the Coulomb branch of an $A_n$ quiver with spin-$\frac32$ half-hypers, and check consistency of a general monopole-antimonopole two-point function.

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arXiv2024

Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs

The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d $\mathcal{N}=2$ superconformal field theories with fractional r-charges, there exists a special notion of high-temperature limit on higher sheets that captures data of three-dimensional topological quantum field theories arising from r-twisted circle reduction. These TQFTs are closely tied with the VOA of the 4d SCFT. We study such high-temperature limits. More specifically, we apply Di~Pietro-Komargodski type supersymmetric effective field theory techniques to r-twisted circle reductions of $(A_1,A_{2n})$ Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest $\mathcal{N}=1$ supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d $\mathcal{N}=2$ SUSY enhancing rank-$0$ theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs $M(2,2n+3)$. Upon topological twist, they give non-unitary TQFTs controlled by the $M(2,2n+3)$ modular tensor category (MTC). The high-temperature limit on other sheets yields their unitary or non-unitary Galois conjugates. This opens up the prospect of a broader four-supercharge perspective on the celebrated correspondence between 4d $\mathcal{N}=2$ SCFTs and 2d VOAs via interpolating 3d EFTs. Several byproducts follow, including a systematic approach to 3d SUSY enhancement from 4d SUSY enhancement, and a 3d QFT handle on Galois orbits of various MTCs associated with 4d $\mathcal{N}=2$ SCFTs.

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arXiv2024

Ising BCFT from Fuzzy Hemisphere

We extend the recently introduced fuzzy sphere technique for the 3d Ising CFT to the case of boundary CFT (BCFT) using the fuzzy hemisphere. This allows to study conformal boundary conditions, and we investigate the three boundary universality classes of the 3d Ising CFT. These include the ordinary, extraordinary, and special boundary conditions. We identify the qualitative signatures of boundary conformal invariance, and in the cases of ordinary and extraordinary boundary conditions, obtain numerical estimates for the spectrum of low-lying boundary primaries. For the special boundary conditions, we are only able to see their qualitative features, while reliable estimates of the scaling dimensions of boundary primaries are left for the future work.

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arXiv2024

Chiral life on a slab

We study chiral algebra in the reduction of 3D $\mathcal{N} = 2 $ supersymmetric gauge theories on an interval with the $\mathcal{N}=(0,2)$ Dirichlet boundary conditions on both ends. By invoking the 3D ``twisted formalism'' and the 2D $βγ$-description we explicitly find the perturbative $\overline{Q}_+$ cohomology of the reduced theory. It is shown that the vertex algebras of boundary operators are enhanced by the line operators. A full non-perturbative result is found in the abelian case, where the chiral algebra is given by the rank two Narain lattice VOA, and two more equivalent descriptions are provided. Conjectures and speculations on the nonperturbative answer in the non-abelian case are also given.

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arXiv2024

On the 4d/3d/2d view of the SCFT/VOA correspondence

We start with the SCFT/VOA correspondence formulated in the Omega-background approach, and connect it to the boundary VOA in 3d $\mathcal{N}=4$ theories and chiral algebras of 2d $\mathcal{N}=(0,2)$ theories. This is done using the dimensional reduction of the 4d theory on the topologically twisted and Omega-deformed cigar, performed in two steps. This paves the way for many more interesting questions, and we offer quite a few. We also use this approach to explain some older observations on the TQFTs produced from the generalized Argyres-Douglas (AD) theories reduced on the circle with a discrete twist. In particular, we argue that many AD theories with trivial Higgs branch, upon reduction on $S^1$ with the $\mathbb{Z}_N$ twist (where $\mathbb{Z}_N$ is a global symmetry of the given AD theory), result in the rank-0 3d $\mathcal{N}=4$ SCFTs, which have been a subject of recent studies. A generic AD theory, by the same logic, leads to a 3d $\mathcal{N}=4$ SCFT with zero-dimensional Coulomb branch (and suggests that there are a lot of them). Our construction therefore puts various empirical observations on the firm ground, such as, among other things, the match between the 4d VOA and the boundary VOA for some 3d rank-0 SCFTs previously observed in the literature. We end with an extensive list of promising open problems.

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arXiv2023

Remarks on Berry Connection in QFT, Anomalies, and Applications

Berry connection has been recently generalized to higher-dimensional QFT, where it can be thought of as a topological term in the effective action for background couplings. Via the inflow, this term corresponds to the boundary anomaly in the space of couplings, another notion recently introduced in the literature. In this note we address the question of whether the old-fashioned Berry connection (for time-dependent couplings) still makes sense in a QFT on $Σ^{(d)}\times \mathbb{R}$, where $Σ^{(d)}$ is a $d$-dimensional compact space and $\mathbb{R}$ is time. Compactness of $Σ^{(d)}$ relieves us of the IR divergences, so we only have to address the UV issues. We describe a number of cases when the Berry connection is well defined (which includes the $tt^*$ equations), and when it is not. We also mention a relation to the boundary anomalies and boundary states on the Euclidean $Σ^{(d)} \times \mathbb{R}_{\geq 0}$. We then work out the examples of a free 3D Dirac fermion and a 3D $\mathcal{N}=2$ chiral multiplet. Finally, we consider 3D theories on $\mathbb{T}^2\times \mathbb{R}$, where the space $\mathbb{T}^2$ is a two-torus, and apply our machinery to clarify some aspects of the relation between 3D SUSY vacua and elliptic cohomology. We also comment on the generalization to higher genus.

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arXiv2023

Interfaces and Quantum Algebras, II: Cigar Partition Function

The supersymmetric cigar (half-)index or cigar partition function of 3d $\mathcal{N}=2$ gauge theories contains a wealth of information. Physically, it captures the spectrum of BPS states, the non-perturbative corrections to various partition functions, the effective twisted superpotential and the data of supersymmetric vacua. Mathematically, it defines the K-theoretic Vertex counting vortices/quasimaps, and connects to quantum K-theory, as well as elliptic cohomology and stable envelopes. We explore these topics from the physics standpoint, systematically developing the foundations and explaining various mathematical properties using the quantum field theory machinery.

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arXiv2023

Interfaces and Quantum Algebras, I: Stable Envelopes

The stable envelopes of Okounkov et al. realize some representations of quantum algebras associated to quivers, using geometry. We relate these geometric considerations to quantum field theory. The main ingredients are the supersymmetric interfaces in gauge theories with four supercharges, relation of supersymmetric vacua to generalized cohomology theories, and Berry connections. We mainly consider softly broken compactified three dimensional $\mathcal{N} =4$ theories. The companion papers will discuss applications of this construction to symplectic duality, Bethe/gauge correspondence, generalizations to higher dimensional theories, and other topics.

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arXiv2023

Snowmass White Paper: The Quest to Define QFT

This article provides a review of the literature on rigorous definitions and constructions in Quantum Field Theory, spanning the period of seven decades. Comparing with the ideas and constructions found in the modern physics literature, we conclude that none of the existing systems of QFT axioms can cover all the physical situations. Therefore, it is still an outstanding open problem to formulate a complete definition of QFT. We argue that the question is of relevance for both physicists and mathematicians.

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arXiv2023

Interval reduction and (super)symmetry

We study three-dimensional quantum field theories on the interval with symmetry-preserving boundary conditions. The physics and symmetries of the effective 2D theory in the IR are the main subjects of this note. We focus on the (super-)Yang-Mills-Chern-Simons (YM-CS) theories with the Dirichlet boundary conditions on both ends. We warm up with the $\mathcal{N}=0$ and $\mathcal{N}=1$ cases flowing to the bosonic and $\mathcal{N}=(0,1)$ WZW models in 2D. Then we study the 3D $\mathcal{N}=2$ YM-CS on the interval with the $\mathcal{N}=(0,2)$ Dirichlet boundaries. It flows to a non-compact version of the $\mathcal{N}=(0,2)$ WZW. We compute its perturbatively exact two-derivative effective action (i.e., the metric and the B-field), and speculate on the possibility of novel non-perturbative effects. We also construct the 2D Landau-Ginzburg models flowing to the similar sigma models.

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arXiv2021

Gluing II: Boundary Localization and Gluing Formulas

We describe applications of the gluing formalism discussed in the companion paper. When a $d$-dimensional local theory $\text{QFT}_d$ is supersymmetric, and if we can find a supersymmetric polarization for $\text{QFT}_d$ quantized on a $(d-1)$-manifold $W$, gluing along $W$ is described by a non-local $\text{QFT}_{d-1}$ that has an induced supersymmetry. Applying supersymmetric localization to $\text{QFT}_{d-1}$, which we refer to as the boundary localization, allows in some cases to represent gluing by finite-dimensional integrals over appropriate spaces of supersymmetric boundary conditions. We follow this strategy to derive a number of `gluing formulas' in various dimensions, some of which are new and some of which have been previously conjectured. First we show how gluing in supersymmetric quantum mechanics can reduce to a sum over a finite set of boundary conditions. Then we derive two gluing formulas for 3D $\mathcal{N}=4$ theories on spheres: one providing the Coulomb branch representation of gluing, and another providing the Higgs branch representation. This allows to study various properties of their $(2,2)$-preserving boundary conditions in relation to Mirror Symmetry. After that we derive a gluing formula in 4D $\mathcal{N}=2$ theories on spheres, both squashed and round. First we apply it to predict the hemisphere partition function, then we apply it to the study of boundary conditions and domain walls in these theories. Finally, we mention how to glue half-indices of 4D $\mathcal{N}=2$ theories.

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arXiv2021

From VOAs to short star products in SCFT

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 $S^3\times S^1$: 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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arXiv2020

Correlators on the wall and $\mathfrak{sl}_n$ spin chain

We study algebras and correlation functions of local operators at half-BPS interfaces engineered by the stacks of D5 or NS5 branes in the 4d $\mathcal{N}=4$ super Yang-Mills. The operator algebra in this sector is isomorphic to a truncation of the Yangian $\mathcal{Y}(\mathfrak{gl}_n)$. The correlators, encoded in a trace on the Yangian, are controlled by the inhomogeneous $\mathfrak{sl}_n$ spin chain, where $n$ is the number of fivebranes: they are given in terms of matrix elements of transfer matrices associated to Verma modules, or equivalently of products of Baxter's Q-operators. This can be viewed as a novel connection between the $\mathcal{N}=4$ super Yang-Mills and integrable spin chains. We also remark on analogous constructions involving half-BPS Wilson lines.

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arXiv2020

Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM

We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d $\mathcal{N}=4$ super Yang-Mills with the gauge group $G$, which are described by associative algebras equipped with twisted traces. Such data are in one-to-one correspondence with an infinite set of defect correlation functions. We identify algebras and traces for known boundary conditions. Ward identities expressing the (twisted) periodicity of the trace highly constrain its structure, in many cases allowing for the complete solution. Our main examples in this paper are: the universal enveloping algebra $U(\mathfrak{g})$ with the trace describing the Dirichlet boundary conditions; and the finite W-algebra $\mathcal{W}(\mathfrak{g},t_+)$ with the trace describing the Nahm pole boundary conditions.

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arXiv2019

4d/2d $\rightarrow $ 3d/1d: A song of protected operator algebras

Superconformal field theories (SCFT) are known to possess solvable yet nontrivial sectors in their full operator algebras. Two prime examples are the chiral algebra sector on a two dimensional plane in four dimensional $\mathcal{N}=2$ SCFTs, and the topological quantum mechanics (TQM) sector on a line in three dimensional $\mathcal{N}=4$ SCFTs. Under Weyl transformation, they respectively map to operator algebras on a great torus in $S^1\times S^3$ and a great circle in $S^3$, and are naturally related by reduction along the $S^1$ factor, which amounts to taking the Cardy (high-temperature) limit of the four dimensional theory on $S^1\times S^3$. We elaborate on this relation by explicit examples that involve both Lagrangian and non-Lagrangian theories in four dimensions, where the chiral algebra sector is generally described by a certain W-algebra, while the three dimensional descendant SCFT always has a (mirror) Lagrangian description. By taking into account a subtle R-symmetry mixing, we provide explicit dictionaries between selected operator product expansion (OPE) data in the four and three dimensional SCFTs, which we verify in the examples using recent localization results in four and three dimensions. Our methods thus provide nontrivial support for various chiral algebra proposals in the literature. Along the way, we also identify three dimensional mirrors for Argyres-Douglas theories of type $(A_1, D_{2n+1})$ reduced on $S^1$, and find more evidence for earlier proposals in the case of $(A_1, A_{2n-2})$, which both realize certain superconformal boundary conditions for the four dimensional $\mathcal{N}=4$ super-Yang-Mills. This is a companion paper to arXiv:1911.05741.

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arXiv2019

Chiral Algebra, Localization, Modularity, Surface defects, And All That

We study the 2D vertex operator algebra (VOA) construction in 4D $\mathcal{N}=2$ superconformal field theories (SCFT) on $S^3 \times S^1$, focusing both on old puzzles as well as new observations. The VOA lives on a two-torus $\mathbb{T}^2\subset S^3\times S^1$, it is $\frac12\mathbb{Z}$-graded, and this torus is equipped with the natural choice of spin structure (1,0) for the $\mathbb{Z} +\frac12$-graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserve the VOA, we find that it admits discrete deformations, which allow access to the remaining spin structures (1,1), (0,1) and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle, the two-point functions, and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the $T$-transformation acts on our four partition functions and lifts to a large diffeomorphism on $S^3\times S^1$. More interestingly, we generalize the four partition functions on the torus to an infinite family labeled both by the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the $S$-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the $Ω$-background.

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arXiv2018

Coulomb Branch Quantization and Abelianized Monopole Bubbling

We develop an approach to the study of Coulomb branch operators in 3D $\mathcal{N}=4$ gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For `good' and `ugly' theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.

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arXiv2018

3d TQFTs from Argyres-Douglas theories

We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1 \times M_3$ with a non-trivial holonomy of a discrete global symmetry along the $S^1$. For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern-Simons and Rozansky-Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as the $(G_2)_1$ and $(F_4)_1$ Chern-Simons theories. Our construction is based on an intriguing relation between topologically twisted partition functions, wild Hitchin characters, and chiral algebras which, when combined together, relate Coulomb branch and Higgs branch data of the same 4d $\mathcal{N}=2$ theory. We test our proposal by applying localization techniques to the conjectural $\mathcal{N}=1$ UV Lagrangian descriptions of the $(A_1,A_2)$, $(A_1,A_3)$ and $(A_1,D_3)$ theories.

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