scholarly journals Quantum integrable systems from supergroup gauge theories

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Heng-Yu Chen ◽  
Taro Kimura ◽  
Norton Lee
Keyword(s):  
Partition Function ◽  
Integrable Systems ◽  
Spin Chain ◽  
Toda Lattice ◽  
Gauge Theories ◽  
Partition Functions ◽  
Characteristic Polynomials ◽  
Quantum Integrable Systems ◽  
Gauge Groups ◽  
Moser System

Abstract In this note, we establish several interesting connections between the super- group gauge theories and the super integrable systems, i.e. gauge theories with supergroups as their gauge groups and integrable systems defined on superalgebras. In particular, we construct the super-characteristic polynomials of super-Toda lattice and elliptic double Calogero-Moser system by considering certain orbifolded instanton partition functions of their corresponding supergroup gauge theories. We also derive an exotic generalization of 𝔰𝔩(2) XXX spin chain arising from the instanton partition function of SQCD with super- gauge group, and study its Bethe ansatz equation.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals MODIFIED PARTITION FUNCTIONS, CONSISTENT ANOMALIES AND CONSISTENT SCHWINGER TERMS

2011 ◽  
Vol 08 (08) ◽  
pp. 1747-1762 ◽  
Author(s):  
AMIR ABBASS VARSHOVI
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Partition Functions ◽  
Gauge Invariant

A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally.

scholarly journals Topological vertex for 6d SCFTs with ℤ2-twist

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hee-Cheol Kim ◽  
Minsung Kim ◽  
Sung-Soo Kim
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Outer Automorphism ◽  
Elliptic Genus ◽  
Partition Functions ◽  
Topological Vertex

Abstract We compute the partition function for 6d $$ \mathcal{N} $$ N = 1 SO(2N) gauge theories compactified on a circle with ℤ2 outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5-planes. As representative examples, we consider 6d SO(8) and SU(3) gauge theories with ℤ2 twist. We confirm that these partition functions obtained from the topological vertex with O5-planes indeed agree with the elliptic genus computations.

scholarly journals Decomposition of BPS moduli spaces and asymptotics of supersymmetric partition functions

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Arash Arabi Ardehali ◽  
Junho Hong
Keyword(s):  
Partition Function ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Gauge Theories ◽  
Asymptotic Expression ◽  
Effective Field ◽  
Asymptotic Result ◽  
Partition Functions ◽  
Abelian Gauge ◽  
Scale Hierarchy

Abstract We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by i) decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off Λ) they support, ii) localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and iii) summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as Λ → ∞). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS5/CFT4. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results.

scholarly journals More on topological vertex formalism for 5-brane webs with O5-plane

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Rui-Dong Zhu
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Vertex Operator ◽  
Vertex Function ◽  
Gauge Theories ◽  
Partition Functions ◽  
Topological Vertex ◽  
Concrete Form ◽  
Nekrasov Partition Functions ◽  
Chern Simons

Abstract We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of [1]. Using the O-vertex it is possible to compute the Nekrasov partition functions of 5d theories realized on any 5-brane web diagrams with O5-planes. We apply our proposal to 5-brane webs with an O5-plane and compute the partition functions of pure SO(N) gauge theories and the pure G2 gauge theory. The obtained results agree with the results known in the literature. We also compute the partition function of the pure SU(3) gauge theory with the Chern-Simons level 9. At the end we rewrite the O-vertex in a form of a vertex operator.

scholarly journals Surface defects on E-string from 5-brane webs

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Sung-Soo Kim ◽  
Yuji Sugimoto ◽  
Futoshi Yagi
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Surface Defect ◽  
Gauge Theories ◽  
Surface Defects ◽  
Elliptic Genus ◽  
Partition Functions ◽  
Global Symmetry ◽  
Geometric Transition ◽  
Supersymmetric Gauge

Abstract We study 6d E-string theory with defects on a circle. Our basic strategy is to apply the geometric transition to the supersymmetric gauge theories. First, we calculate the partition functions of the 5d SU(3)0 gauge theory with 10 flavors, which is UV-dual to the 5d Sp(2) gauge theory with 10 flavors, based on two different 5-brane web diagrams, and check that two partition functions agree with each other. Then, by utilizing the geometric transition, we find the surface defect partition function for E-string on ℝ4 × T2. We also discuss that our result is consistent with the elliptic genus. Based on the result, we show how the global symmetry is broken by the defects, and discuss that the breaking pattern depends on where/how we insert the defects.

scholarly journals Partition functions of Chern-Simons theory on handlebodies by radial quantization

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Massimo Porrati ◽  
Cedric Yu
Keyword(s):  
Partition Function ◽  
Riemann Surfaces ◽  
Wilson Loop ◽  
Transition Amplitude ◽  
Simons Theory ◽  
Partition Functions ◽  
Initial State ◽  
Gauge Groups ◽  
Arbitrary Genus ◽  
Chern Simons

Abstract We use radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus. The partition function is given by a particular transition amplitude between two states which are defined on the Riemann surfaces that define the (singular) foliation of the handlebody. The final state is a coherent state while on the initial state the holonomy operator has zero eigenvalue. The latter choice encodes the constraint that the gauge fields must be regular everywhere inside the handlebody. By requiring that the only singularities of the gauge field inside the handlebody must be compatible with Wilson loop insertions, we find that the Wilson loop shifts the holonomy of the initial state. Together with an appropriate choice of normalization, this procedure selects a unique state in the Hilbert space obtained from a Kähler quantization of the theory on the constant-radius Riemann surfaces. Radial quantization allows us to find the partition functions of Abelian Chern-Simons theories for handlebodies of arbitrary genus. For non-Abelian compact gauge groups, we show that our method reproduces the known partition function at genus one.

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