首页/论文/2012.15352

arXiv 2012.153522020-12-30hep-thmath-phmath.MP

4d higgsed network calculus and elliptic DIM algebra

Mohamed Ghoneim, Can Kozçaz, Kerem Kurşun, Yegor Zenkevich

备注：: 23 pages, 1 figure

英文摘要：

Supersymmetric gauge theories of certain class possess a large hidden nonperturbative symmetry described by the Ding-Iohara-Miki (DIM) algebra which can be used to compute their partition functions and correlators very efficiently. We lift the DIM-algebraic approach developed to study holomorphic blocks of 3d linear quiver gauge theories one dimension higher. We employ an algebraic construction in which the underlying trigonometric DIM algebra is elliptically deformed, and an alternative geometric approach motivated by topological string theory. We demonstrate the equivalence of these two methods, and motivated by this, prove that elliptic DIM algebra is isomorphic to the direct sum of a trigonometric DIM algebra and an additional Heisenberg algebra.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Higgsed network calculus

We introduce a formalism for describing holomorphic blocks of 3d quiver gauge theories using networks of Ding-Iohara-Miki algebra intertwiners. Our approach is very direct and gives an explicit identification of the blocks with Dotsenko-Fateev type integrals for q-deformed quiver W-algebras. We also explain how quiver theories corresponding to Dynkin diagrams of superalgebras arise, write down the corresponding partition functions and W-algebras, and explain the connection with supersymmetric Macdonald-Ruijsenaars commuting Hamiltonians.

2021-05-11hep-thmath-phmath.MP

Mixed network calculus

We show how to combine higgsed topological vertices introduced in our previous work with conventional refined topological vertices. We demonstrate that the extended formalism describes very general interacting D5-NS5-D3 brane systems. In particular, we introduce new types of intertwining operators of Ding-Iohara-Miki algebra between different types of Fock representations corresponding to the crossings of NS5 and D5 branes. As a byproduct we obtain an algebraic description of the Hanany-Witten brane creation effect, give an efficient recipe to compute the brane factors in 3d N=2 and N=4 quiver…

2020-12-31hep-thmath-phmath.MP

可积系统与广义环形多边形及被Higgs化的5维N=1理论

Integrable Systems for Generalized Toric Polygons and Higgsed 5d N=1 Theories

Ulsan National Institute of Science and Technology（蔚山科学技术院）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京数学与交叉科学研究院）；Center for Geometry and Physics, Institute for Basic Science (IBS)（基础科学研究院几何物理中心）

研究广义环形多边形的可积系统及其与5维量子场论的关系，通过精细的birational变换构建Higgs化的N=1理论。

2026-03-19hep-thmath-phmath.AG

Exact partition functions of Higgsed 5d $T_N$ theories

We present a general prescription by which we can systematically compute exact partition functions of five-dimensional supersymmetric theories which arise in Higgs branches of the $T_N$ theory. The theories may be realized by webs of 5-branes whose dual geometries are non-toric. We have checked our method by calculating the partition functions of the theories realized in various Higgs branches of the $T_3$ theory. A particularly interesting example is the $E_8$ theory which can be obtained by Higgsing the $T_6$ theory. We explicitly compute the partition function of the $E_8$ theory and find t…

2015-01-19hep-th

Generalized Cartan Calculus in general dimension

We develop the generalized Cartan Calculus for the groups $G=$SL$(2,\mathbb{R})\times\mathbb{R}^+$, SL$(5,\mathbb{R})$ and SO(5,5). They are the underlying algebraic structures of $d=9,7,6$ exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincaré lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

2015-06-18hep-thmath-phmath.MP

An infinite-dimensional calculus for gauge theories

A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior on nongeneric strata is also obtained.

2010-05-08hep-thmath-phmath.FA

更多相关论文收起更多论文

Finite dimensional quantum group covariant differential calculus on a complex matrix algebra

Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken as a reduced quantum plane, we build a differential calculus Omega(S) on the quantum space S defined by the algebra C^\infty(M) \otimes M(3,C), where M is a space-time manifold. This calculus is covariant under the action and coaction of finite dimensional dual quantum groups. We study the star structures on these quantum groups and the compatible one in M(3,C). This leads to an invariant scalar product on the later space. We analyse the differential algebra Omega(M(3,C)) in terms of quantum group representations, an…

1998-04-03hep-thmath-phmath.MP

Deconstruction of the Maldacena-Nunez Compactification

We demonstrate a classical equivalence between the large-N limit of the Higgsed N=1* SUSY U(N) Yang-Mills theory and the Maldacena-Nunez twisted compactification of a six dimensional gauge theory on a two-sphere. A direct comparison of the actions and spectra of the two theories reveals them to be identical. We also propose a gauge theory limit which should describe the corresponding spherical compactification of Little String Theory.

2006-04-28hep-th

Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces

We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four dimensional space.

2018-05-16hep-thmath-phmath.MP

Global Anomalies and Geometric Engineering of Critical Theories in Six Dimensions

We show the existence of global gauge anomalies in six dimensions for gauge groups SU(2),SU(3) and G_2 coupled to matter, characterized by an element of Z_{12},Z_6 and Z_3 respectively. Consideration of this anomaly rules out some of the recently proposed 6 dimensional N=1 QFT's which were conjectured to possess IR fixed point at infinite coupling. We geometrically engineer essentially all the other models with one tensor multiplet using F-theory. In addition we construct 3 infinite series using F-theory geometry which do not have field theory analogs. All these models in the maximally Higgsed…

1997-03-25hep-th

规范理论的带状ZX演算

A ribbon ZX calculus for gauge theory

University of Oxford（牛津大学）

本文将ZX演算推广到紧致规范群的二维杨-米尔斯理论，利用Hopf Frobenius代数结构建立与二维拓扑量子场论的联系，为低维引力应用铺路。

2026-06-12cond-mat.otherhep-thmath-ph

A New Infinite Class of Quiver Gauge Theories

We construct a new infinite family of N=1 quiver gauge theories which can be Higgsed to the Y^{p,q} quiver gauge theories. The dual geometries are toric Calabi-Yau cones for which we give the toric data. We also discuss the action of Seiberg duality on these quivers, and explore the different Seiberg dual theories. We describe the relationship of these theories to five dimensional gauge theories on (p,q) 5-branes. Using the toric data, we specify some of the properties of the corresponding dual Sasaki-Einstein manifolds. These theories generically have algebraic R-charges which are not quadrat…

2005-03-24hep-th

Three Dimensional Differential Calculus on the Quantum Group SU_q(2) and Minimal Gauge Theory

Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed Lie algebras are obtained in terms of differential operators. The consistent gauge covariant differential calculus on SU_q(2) is uniquely defined. A non-standard Leibnitz rule is proposed for the exterior differential. The minimal gauge theory with SU_q(2) quantum group symmetry is considered.

1999-12-20hep-th

Supergravity Tensor Calculus in 5D from 6D

Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus still retains the dilatation gauge symmetry so that it becomes a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system.

2000-10-26hep-phhep-th

Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories

We demonstrate electric-magnetic duality in N=1 supersymmetric non-Abelian gauge theories in four dimensions by presenting two different gauge theories (different gauge groups and quark representations) leading to the same non-trivial long distance physics. The quarks and gluons of one theory can be interpreted as solitons (non-Abelian magnetic monopoles) of the elementary fields of the other theory. The weak coupling region of one theory is mapped to a strong coupling region of the other. When one of the theories is Higgsed by an expectation value of a squark, the other theory is confined. Ma…

1994-11-20hep-phhep-th

Spinor calculus for q-deformed quantum spaces II

This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. The Clifford algebras corresponding to these quantum spaces are treated. Especially, their commutation relations and their Hopf structures are written down. Bases of the four-dimensional Clifford algebras are constructed and their properties are discussed. Matrix representations of the Clifford algebras lead to q-deformed Dirac-matrices for the four-d…

2007-05-11hep-th

Contracted Bianchi Identity and Angle Relation on n-dimensional Simplicial Complex of Regge Calculus

In this article, we prove the theorems concerning the trace relation of SO(3), SU(2), and SO(n) which are representation of SO(3) and SU(2). An interesting fact we found is the trace relation of SU(2) gives the spherical law of cosine which in turns is a dihedral angle relation, a constraint that must be satisfied by closed Euclidean simplices. Moreover, we applied our results on general group elements to holonomies on the simplicial complex of Regge Calculus, which is the main motivation of this article. Here, we found that: (1) in 4-dimensional Euclidean Regge Gravity, all the holonomy circl…

2018-07-30gr-qchep-th

Differential calculus and gauge theory on finite sets

We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential ingredient of his reformulation of the standard model of elementary particle physics) is recovered in our approach. Reductions of the universal differential calculus to `lower-dimensional' differential calculi are considered. The `complete reduction' leads to a differential calculus on a periodic lattice which is related to q-calculus.

1994-01-28hep-th

Partition functions of N=(2,2) gauge theories on S^2 and vortices

We apply localization techniques to compute the partition function of a two-dimensional N=(2,2) R-symmetric theory of vector and chiral multiplets on S^2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet-Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. As applicat…

2014-08-26hep-th

Exotic Gauge Theories from Tensor Calculus

We construct non-standard interactions between exterior form gauge fields by gauging a particular global symmetry of the Einstein-Maxwell action for such fields. Furthermore we discuss generalizations of such interactions by adding couplings to gravitational Chern-Simons forms and to fields arising through dimensional reduction. The construction uses an appropriate tensor calculus.

2000-01-30hep-th

Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories

The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus~(NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the ``Chern character'' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimen…

1999-11-09hep-lathep-th