A taxonomy of twists of supersymmetric Yang–Mills theory

Elliott, Chris; Safronov, Pavel; Williams, Brian R.

doi:10.1007/s00029-022-00786-y

Cited by 13 publications

(8 citation statements)

References 70 publications

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“…Early examples include [6][7][8] and this technique has been systematically developed in e.g. [9,10] recently. After such a twist, the resulting theories become holomorphic in most space time directions.…”

Section: Introductionmentioning

confidence: 99%

Monopole operators and bulk-boundary relation in holomorphic topological theories

Zeng

2023

SciPost Phys.

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We study the holomorphic twist of 3d3dN = 2N=2 supersymmetric field theories, discuss the perturbative bulk local operators in general, and explicitly construct non perturbative bulk local operators for abelian gauge theories. Our construction is verified by matching the character of the algebra with the superconformal index. We test a conjectural relation between the derived center of boundary algebras and bulk algebras in various cases, including Landau-Ginzburg models with an arbitrary superpotential and some abelian gauge theories. In the latter cases, monopole operators appear in the derived center of a perturbative boundary algebra. We briefly discuss the higher structures in both boundary and bulk algebras.

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Section: Introductionmentioning

confidence: 99%

Monopole operators and bulk-boundary relation in holomorphic topological theories

Zeng

2023

SciPost Phys.

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“…This is exactly the holomorphic-topological twist of six-dimensional N = (1, 1) super Yang-Mills theory, dubbed the rank (1, 1) partially holomorphic topological twist in [77].…”

Section: A2 Topological Open String Field Theorymentioning

confidence: 98%

Superspin chains from superstring theory

Ishtiaque¹,

Moosavian

Raghavendran

et al. 2022

SciPost Phys.

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We present a correspondence between two-dimensional \mathcal{N} = (2,2)𝒩=(2,2) supersymmetric gauge theories and rational integrable \mathfrak{gl}(m|n)𝔤𝔩(m|n) spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern–Simons theory with gauge group GL(m|n)GL(m|n). The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational \mathfrak{gl}(m|n)𝔤𝔩(m|n) spin chains with spins valued in finite-dimensional representations.

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“…By the results of [52], they efficiently and fully encode the information of the various twists of the original multiplet M : one can compute the stalk of the module at a classical point Q : C • (n, E) → C, obtaining descriptions of different twists for different orbits under the action of Spin(n) and the group of R-symmetries. We refer to the discussion in [20,22,23] for details of this classification. It would, for example, be interesting to explicitly understand the modules associated to multiplets such as the N = (1, 0) tensor multiplet in six dimensions.…”

Section: Further Directionsmentioning

confidence: 99%

“…This idea goes back to the beginnings of the BV formalism; applications to global symmetries are discussed, for example, in [3]. The example of super Yang-Mills theory is discussed rigorously and systematically in all dimensions in [23].…”

Section: Homotopy Theory Of Multipletsmentioning

confidence: 99%

The Derived Pure Spinor Formalism as an Equivalence of Categories

Elliott¹,

Hahner²,

Saberi³

2023

SIGMA

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We construct a derived generalization of the pure spinor superfield formalism and prove that it exhibits an equivalence of dg-categories between multiplets for a supertranslation algebra and equivariant modules over its Chevalley-Eilenberg cochains. This equivalence is closely linked to Koszul duality for the supertranslation algebra. After introducing and describing the category of supermultiplets, we define the derived pure spinor construction explicitly as a dg-functor. We then show that the functor that takes the derived supertranslation invariants of any supermultiplet is a quasi-inverse to the pure spinor construction, using an explicit calculation. Finally, we illustrate our findings with examples and use insights from the derived formalism to answer some questions regarding the ordinary (underived) pure spinor superfield formalism.

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A taxonomy of twists of supersymmetric Yang–Mills theory

Cited by 13 publications

References 70 publications

Monopole operators and bulk-boundary relation in holomorphic topological theories

Monopole operators and bulk-boundary relation in holomorphic topological theories

Superspin chains from superstring theory

The Derived Pure Spinor Formalism as an Equivalence of Categories

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