Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces

Bruzzo, Ugo; Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.

doi:10.1016/j.aim.2015.11.005

Cited by 36 publications

(113 citation statements)

References 65 publications

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“…These results are mainly due to the application of equivariant localization to the supersymmetric path integral which reduces its evaluation to a combinatorial problem. The results obtained so far concern few examples of four-manifolds as C 2 [12,13], C 2 /Γ [14][15][16][17][18][19][20], S 4 [21,22] and S 2 × S 2 [23].…”

Section: Jhep07(2016)023mentioning

confidence: 99%

Exact results for N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

Bershtein

Bonelli

Ronzani

et al. 2016

J. High Energ. Phys.

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We provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N ) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2 * theory on P 2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

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Section: Jhep07(2016)023mentioning

confidence: 99%

Exact results for N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

Bershtein

Bonelli

Ronzani

et al. 2016

J. High Energ. Phys.

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“…More recently, N = 2 supersymmetric gauge theories on the minimal resolution general toric singularities have been considered [11] in the context of AGT correspondence with two-dimensional (super-)conformal field theories [12]. A rigorous mathematical framework for A n singularities has been presented in [13,14]. Supersymmetric gauge theories with N = 2 on curved four manifolds have been considered for example in [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

N = 2 $$ \mathcal{N}=2 $$ supersymmetric gauge theories on S2 × S2 and Liouville Gravity

Bawane

Bonelli

Ronzani

et al. 2015

J. High Energ. Phys.

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We consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S 2 × S 2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

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“…When M 4 is a toric surface, the general gluing construction, illustrated in (2.4) or (2.14), leads to various extensions of W -algebras for g = Lie(G) of the same type as the original "gauge" group G. Although this general gluing construction is supported by a number of direct calculations [14,16,17,32], which build on the AGT conjecture [25] for M 4 = R 4 1, 2 , it may seem puzzling. Indeed, when G = U (N ) and M 4 is a 4-manifold with a linear plumbing, as in Figure 1:…”

Section: Toric Manifolds and Toroidal Algebrasmentioning

confidence: 99%

“…to bring together various developments where similar vertex algebras appear in closely related physical systems, but have not yet been explicitly connected. Thus, some of the vertex algebras we are going to mention are familiar in the context of the BPS/CFT and AGT correspondence [13,14,15,16,17] and one novelty of the present approach is to interpret even these familiar examples as chiral (left-moving) algebras of 2d superconformal theories T [M 4 ]. Needless to say, it is important to test this proposed interpretation by studying theories T [M 4 ] and verifying that their chiral algebras indeed agree with VOAs discussed here.…”

Section: Introductionmentioning

confidence: 99%