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 Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

scholarly journals The one-loop partition function of super-Yang–Mills theory on

2005 ◽  
Vol 711 (1-2) ◽  
pp. 199-230 ◽  
Author(s):  
Marcus Spradlin ◽  
Anastasia Volovich
Keyword(s):  
Partition Function ◽  
Yang Mills ◽  
The One ◽  
Super Yang Mills Theory

scholarly journals EMERGENCE OF THE HAAR MEASURE IN THE STANDARD FUNCTIONAL INTEGRAL REPRESENTATION OF THE YANG-MILLS PARTITION FUNCTION

1996 ◽  
Vol 11 (30) ◽  
pp. 2451-2461 ◽  
Author(s):  
H. REINHARDT
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Haar Measure ◽  
Transition Amplitude ◽  
Functional Integral ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Gauge Fixing ◽  
Popov Method

The conventional path integral expression for the Yang–Mills transition amplitude with flat measure and gauge-fixing built in via the Faddeev-Popov method has been claimed to fall short of guaranteeing gauge invariance in the nonperturbative regime. We show, however, that it yields the gauge-invariant partition function where the projection onto gauge-invariant wave functions is explicitly performed by integrating over the compact gauge group. In a variant of maximal Abelian gauge the Haar measure arises in the conventional Yang-Mills path integral from the Faddeev-Popov determinant.

scholarly journals Background independent exact renormalisation

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Kevin Falls
Keyword(s):  
Path Integral ◽  
Effective Action ◽  
Beta Function ◽  
Background Field ◽  
Flow Equation ◽  
Renormalisation Group ◽  
Gauge Invariant ◽  
Yang Mills ◽  
The One ◽  
Group Flow

AbstractA geometric formulation of Wilson’s exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent approach to quantum gravity and gauge theories in the continuum. The regularisation is a geometric variant of Slavnov’s scheme consisting of a modified action, which suppresses high momentum modes, supplemented by Pauli–Villars determinants in the path integral measure. An exact renormalisation group flow equation for the Wilsonian effective action is derived by requiring that the path integral is invariant under a change in the cutoff scale while preserving quasi-locality. The renormalisation group flow is defined directly on the space of gauge invariant actions without the need to fix the gauge. We show that the one-loop beta function in Yang–Mills and the one-loop divergencies of General Relativity can be calculated without fixing the gauge. As a first non-perturbative application we find the form of the Yang–Mills beta function within a simple truncation of the Wilsonian effective action.

scholarly journals Observables of the Generalized 2D Yang–Mills Theories on Arbitrary Surfaces: A Path Integral Approach

1997 ◽  
Vol 12 (30) ◽  
pp. 2265-2270 ◽  
Author(s):  
M. Khorrami ◽  
M. Alimohammadi
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Integral Method ◽  
Integral Approach ◽  
Generating Functional ◽  
Yang Mills ◽  
Path Integral Approach ◽  
Nonorientable Surfaces ◽  
Path Integral Method ◽  
Field Strengths

Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) of the generalized 2-D Yang–Mills theories in the Schwinger–Fock gauge. Our calculation is done for arbitrary 2-D orientable, and also nonorientable surfaces.

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 Duality and mock modularity

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Atish Dabholkar ◽  
Pavel Putrov ◽  
Edward Witten
Keyword(s):  
Partition Function ◽  
Elliptic Genus ◽  
Two Dimensions ◽  
Effective Theory ◽  
Coulomb Branch ◽  
Gauge Groups ◽  
Yang Mills ◽  
Holomorphic Anomaly ◽  
Holomorphic Anomaly Equation ◽  
Relevant Field

We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional \mathcal{N} =4𝒩=4 super Yang-Mills theory on \mathbb{CP}^{2}ℂℙ2 for the gauge group SO(3)SO(3) from the path integral of the effective theory on the Coulomb branch. The holomorphic kernel of this equation, which receives contributions only from the instantons, is not modular but ‘mock modular’. The partition function has correct modular properties expected from SS-duality only after including the anomalous nonholomorphic boundary contributions from anti-instantons. Using M-theory duality, we relate this phenomenon to the holomorphic anomaly of the elliptic genus of a two-dimensional noncompact sigma model and compute it independently in two dimensions. The anomaly both in four and in two dimensions can be traced to a topological term in the effective action of six-dimensional (2,0)(2,0) theory on the tensor branch. We consider generalizations to other manifolds and other gauge groups to show that mock modularity is generic and essential for exhibiting duality when the relevant field space is noncompact.

QUANTUM YANG-MILLS THEORY ON ARBITRARY SURFACES

1992 ◽  
Vol 07 (16) ◽  
pp. 3781-3806 ◽  
Author(s):  
MATTHIAS BLAU ◽  
GEORGE THOMPSON
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Two Dimensional ◽  
Expectation Values ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Integral Methods ◽  
Closed Surfaces ◽  
Abelian Case

We study quantum Maxwell and Yang-Mills theory on orientable two-dimensional surfaces with an arbitrary number of handles and boundaries. Using path integral methods we derive general and explicit expressions for the partition function and expectation values of contractible and noncontractible Wilson loops on closed surfaces of any genus, as well as for the kernels on manifolds with handles and boundaries. In the Abelian case we also compute correlation functions of intersecting and self-intersecting loops on closed surfaces, and discuss the role of large gauge transformations and topologically nontrivial bundles.

scholarly journals On a path integral representation of the Nekrasov instanton partition function and its Nekrasov–Shatashvili limit

2014 ◽  
Vol 92 (3) ◽  
pp. 267-270 ◽  
Author(s):  
Franco Ferrari ◽  
Marcin Piątek
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Path Integral ◽  
Equation Of Motion ◽  
Field Theories ◽  
Integral Expression ◽  
Path Integral Representation ◽  
Yang Mills ◽  
Fundamental Matter ◽  
Mills Field

In this work we study the Nekrasov–Shatashvili limit of the Nekrasov instanton partition function of Yang–Mills field theories with 𝒩 = 2 supersymmetry and gauge group SU(N). The theories are coupled with fundamental matter. A path integral expression of the full instanton partition function is derived. It is checked that in the Nekrasov–Shatashvili (thermodynamic) limit the action of the field theory obtained in this way reproduces exactly the equation of motion used in the saddle-point calculations.

scholarly journals The integrable (hyper)eclectic spin chain

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changrim Ahn ◽  
Matthias Staudacher
Keyword(s):  
Spin Chain ◽  
Nearest Neighbor ◽  
Inverse Scattering Method ◽  
Spin Chains ◽  
Scattering Method ◽  
Yang Mills ◽  
Deformation Parameters ◽  
Dilatation Operator ◽  
The One ◽  
State Spin

Abstract We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills Theory.

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