scholarly journals Refined topological vertex for a 5D Sp(N) gauge theories with antisymmetric matter

2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Shi Cheng ◽  
Sung-Soo Kim
Keyword(s):  
Gauge Theories ◽  
Topological Vertex

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 MacMahon KZ equation for Ding-Iohara-Miki algebra

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Panupong Cheewaphutthisakun ◽  
Hiroaki Kanno
Keyword(s):  
Correlation Function ◽  
Spectral Parameter ◽  
Gauge Theories ◽  
Topological Vertex ◽  
Fock Representation ◽  
Intertwining Operator ◽  
Kz Equation ◽  
Zamolodchikov Equation

Abstract We derive a generalized Knizhnik-Zamolodchikov equation for the correlation function of the intertwiners of the vector and the MacMahon representations of Ding-Iohara-Miki algebra. These intertwiners are cousins of the refined topological vertex which is regarded as the intertwining operator of the Fock representation. The shift of the spectral parameter of the intertwiners is generated by the operator which is constructed from the universal R matrix. The solutions to the generalized KZ equation are factorized into the ratio of two point functions which are identified with generalizations of the Nekrasov factor for supersymmetric quiver gauge theories.

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 6d/5d exceptional gauge theories from web diagrams

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Hee-Cheol Kim ◽  
Kantaro Ohmori
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Partition Functions ◽  
Topological Vertex ◽  
Nekrasov Partition Functions ◽  
Chern Simons ◽  
The Web ◽  
Kaluza Klein

Abstract We construct novel web diagrams with a trivalent or quadrivalent gluing for various 6d/5d theories from certain Higgsings of 6d conformal matter theories on a circle. The theories realized on the web diagrams include 5d Kaluza-Klein theories from circle compactifications of the 6d G2 gauge theory with 4 flavors, the 6d F4 gauge theory with 3 flavors, the 6d E6 gauge theory with 4 flavors and the 6d E7 gauge theory with 3 flavors. The Higgsings also give rise to 5d Kaluza-Klein theories from twisted compactifications of 6d theories including the 5d pure SU(3) gauge theory with the Chern-Simons level 9 and the 5d pure SU(4) gauge theory with the Chern-Simons level 8. We also compute the Nekrasov partition functions of the theories by applying the topological vertex formalism to the newly obtained web diagrams.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

Path integral for gauge theories with fermions

1980 ◽  
Vol 21 (10) ◽  
pp. 2848-2858 ◽  
Author(s):  
Kazuo Fujikawa
Keyword(s):  
Path Integral ◽  
Gauge Theories

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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