Generalized Yang–Mills theory on a Riemann surface

2010 ◽  
pp. 291-306
Author(s):  
Yitzhak Frishman ◽  
Jacob Sonnenschein
Keyword(s):  
Riemann Surface ◽  
Yang Mills

scholarly journals Residues and Topological Yang–Mills Theory in Two Dimensions

1997 ◽  
Vol 09 (01) ◽  
pp. 59-75
Author(s):  
Kenji Mohri
Keyword(s):  
Correlation Function ◽  
Riemann Surface ◽  
Magnetic Flux ◽  
Recursion Relation ◽  
Two Dimensions ◽  
Yang Mills ◽  
Residue Formula ◽  
Valued Field ◽  
Physical Quantities

A residue formula which evaluates any correlation function of topological SUn Yang–Mills theory with arbitrary magnetic flux insertion in two-dimensions are obtained. Deformations of the system by two-form operators are investigated in some detail. The method of the diagonalization of a matrix-valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.

scholarly journals NONPERTURBATIVE EFFECTIVE ACTIONS OF (N=2)-SUPERSYMMETRIC GAUGE THEORIES

1996 ◽  
Vol 11 (11) ◽  
pp. 1929-1973 ◽  
Author(s):  
A. KLEMM ◽  
W. LERCHE ◽  
S. THEISEN
Keyword(s):  
Riemann Surface ◽  
Effective Action ◽  
Gauge Theories ◽  
Gauge Coupling ◽  
Low Energy ◽  
Yang Mills ◽  
Hyperelliptic Riemann Surface ◽  
Supersymmetric Gauge ◽  
Energy Quantum ◽  
Appell Functions

We elaborate on our previous work on (N=2)-supersymmetric Yang-Mills theory. In particular, we show how to explicitly determine the low energy quantum effective action for G=SU(3) from the underlying hyperelliptic Riemann surface, and calculate the leading instanton corrections. This is done by solving Picard-Fuchs equations and asymptotically evaluating period integrals. We find that the dynamics of the SU(3) theory is governed by an Appell system of type F4, and compute the exact quantum gauge coupling explicitly in terms of Appell functions.

PARABOLIC VECTOR BUNDLES AND HERMITIAN-YANG-MILLS CONNECTIONS OVER A RIEMANN SURFACE

1993 ◽  
Vol 04 (03) ◽  
pp. 467-501 ◽  
Author(s):  
JONATHAN A. PORITZ
Keyword(s):  
Riemann Surface ◽  
Vector Bundle ◽  
Sobolev Space ◽  
Moduli Space ◽  
Vector Bundles ◽  
Weighted Sobolev Space ◽  
Conjugacy Classes ◽  
Stable Bundle ◽  
Yang Mills ◽  
Parabolic Bundles

We study a certain moduli space of irreducible Hermitian-Yang-Mills connections on a unitary vector bundle over a punctured Riemann surface. The connections used have non-trivial holonomy around the punctures lying in fixed conjugacy classes of U (n) and differ from each other by elements of a weighted Sobolev space; these connections give rise to parabolic bundles in the sense of Mehta and Seshadri. We show in fact that the moduli space of stable parabolic bundles can be identified with our moduli space of HYM connections, by proving that every stable bundle admits a unique unitary gauge orbit of Hermitian-Yang-Mills connections.

The Narasimhan—Seshadri theorem for parabolic bundles: an orbifold approach

1995 ◽  
Vol 353 (1702) ◽  
pp. 137-171 ◽  
Keyword(s):  
Riemann Surface ◽  
Marked Point ◽  
Weak Compactness ◽  
Analogous Problem ◽  
Rational Approximations ◽  
Higgs Bundles ◽  
Equivalent Problem ◽  
Parabolic Bundle ◽  
Yang Mills ◽  
Parabolic Bundles

Given a stable parabolic bundle over a Riemann surface, we study the problem of finding a compatible Yang-Mills connexion. When the parabolic weights are rational there is an equivalent problem on an orbifold bundle. When the weights are irrational our method is to choose a sequence of approximating rational weights, obtain a corresponding sequence of Yang-Mills connexions on the resulting orbifold bundles and obtain the solution as the limit of this sequence: we need to consider mildly singular connexions which locally about a marked point take the form d — Aid# + a . Here A is a constant diagonal matrix whose entries depend on the weights and their rational approximations, 0 = arg(z) for z a local uniformizing (orbifold) coordinate centred on the marked point and a is an L 2 1 connexion matrix. In this context we find all the necessary gauge-theoretic tools to prove the theorem, including a version of Uhlenbeck’s weak compactness theorem, provided | A| is sufficiently small. (One of the advantages of this approach is that we do analysis on a compact orbifold rather than on the punctured surface.) Our methods also allow us to consider the analogous problem for stable parabolic Higgs bundles.

scholarly journals Localization of four-dimensional super-Yang–Mills theories compactified on Riemann surface

2016 ◽  
Vol 31 (36) ◽  
pp. 1650195
Author(s):  
Koichi Nagasaki
Keyword(s):  
Riemann Surface ◽  
Partition Function ◽  
Path Integral ◽  
Elliptic Genus ◽  
Yang Mills ◽  
The One

We consider the partition function of super-Yang–Mills theories defined on [Formula: see text]. This path integral can be computed by the localization. The one-loop determinant is evaluated by the elliptic genus. This elliptic genus gives trivial result in our calculation. As a result, we obtain a theory defined on the Riemann surface.

scholarly journals PREPOTENTIAL OF N=2 SUPERSYMMETRIC YANG–MILLS THEORIES IN THE WEAK COUPLING REGION

1998 ◽  
Vol 13 (09) ◽  
pp. 1495-1505 ◽  
Author(s):  
TAKAHIRO MASUDA ◽  
HISAO SUZUKI
Keyword(s):  
Riemann Surface ◽  
Weak Coupling ◽  
Quantum Effect ◽  
Low Energy ◽  
Coupling Region ◽  
Yang Mills ◽  
Instanton Contribution ◽  
Hyperelliptic Riemann Surface ◽  
Energy Quantum ◽  
The One

We show how to obtain the explicit form of the low energy quantum effect action for N=2 supersymmetric Yang–Mills theory in the weak coupling region from the underlying hyperelliptic Riemann surface. This is achieved by evaluating the integral representation of the fields explicitly. We calculate the leading instanton corrections for the group SU (Nc), SO (N) and SP (2N) and find that the one-instanton contribution of the prepotentials for these groups coincide with the one obtained recently by using the direct instanton calculation.

scholarly journals The spectrum of marginally-deformed $$ \mathcal{N} $$ = 2 CFTs with AdS4 S-fold duals of type IIB

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Mattia Cesàro ◽  
Gabriel Larios ◽  
Oscar Varela
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Yang Mills ◽  
Conformal Field ◽  
Operator Spectrum ◽  
Two Parameter ◽  
Kaluza Klein

Abstract A holographic duality was recently established between an $$ \mathcal{N} $$ N = 4 non-geometric AdS4 solution of type IIB supergravity in the so-called S-fold class, and a three- dimensional conformal field theory (CFT) defined as a limit of $$ \mathcal{N} $$ N = 4 super-Yang-Mills at an interface. Using gauged supergravity, the $$ \mathcal{N} $$ N = 2 conformal manifold (CM) of this CFT has been assessed to be two-dimensional. Here, we holographically characterise the large-N operator spectrum of the marginally-deformed CFT. We do this by, firstly, providing the algebraic structure of the complete Kaluza-Klein (KK) spectrum on the associated two-parameter family of AdS4 solutions. And, secondly, by computing the $$ \mathcal{N} $$ N = 2 super-multiplet dimensions at the first few KK levels on a lattice in the CM, using new exceptional field theory techniques. Our KK analysis also allows us to establish that, at least at large N, this $$ \mathcal{N} $$ N = 2 CM is topologically a non-compact cylindrical Riemann surface bounded on only one side.

scholarly journals QCD INSTANTONS AND 2D SURFACES

1992 ◽  
Vol 07 (11) ◽  
pp. 1001-1008 ◽  
Author(s):  
V.G.J. RODGERS
Keyword(s):  
Riemann Surface ◽  
Axial Symmetry ◽  
Riemann Surfaces ◽  
Coadjoint Orbits ◽  
Holomorphic Maps ◽  
Topological Information ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Relationship ◽  
Effective Description

Some time ago, Atiyah showed that there exists a natural identification between the k-instantons of a Yang-Mills theory with gauge group G and the holomorphic maps from CP1 to ΩG. Since then, Nair and Mazur have associated the Θ vacua structure in QCD with self-intersecting Riemann surfaces immersed in four dimensions. From here they concluded that these 2D surfaces correspond to the non-perturbative phase of QCD and carry the topological information of the Θ vacua. In this paper we would like to elaborate on this point by making use of Atiyah’s identification. We will argue that an effective description of QCD may be more like a WZW model coupled to the induced metric of an immersion of a 2D Riemann surface in R4. We make some further comments on the relationship between the coadjoint orbits of the Kac-Moody group on G and instantons with axial symmetry and monopole charge.

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