scholarly journals Seiberg duality, quiver gauge theories, and Ihara’s zeta function

2015 ◽  
Vol 30 (18n19) ◽  
pp. 1550118 ◽  
Author(s):  
Da Zhou ◽  
Yan Xiao ◽  
Yang-Hui He
Keyword(s):  
Gauge Theory ◽  
Zeta Function ◽  
Generating Function ◽  
Riemann Hypothesis ◽  
Gauge Theories ◽  
Duality Transformations ◽  
Distribution Of Poles ◽  
Seiberg Duality ◽  
Refined Version

We study Ihara’s zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara’s zeta function to be the generating function for the generic superpotential of the gauge theory.

scholarly journals Spectra of elliptic potentials and supersymmetric gauge theories

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Wei He
Keyword(s):  
Gauge Theory ◽  
Strong Coupling ◽  
Moduli Space ◽  
Gauge Theories ◽  
Duality Transformations ◽  
Spectral Solution ◽  
Supersymmetric Gauge ◽  
Strong Coupling Expansions ◽  
Surface Operator ◽  
Function Potential

Abstract We study a relation between asymptotic spectra of the quantum mechanics problem with a four components elliptic function potential, the Darboux-Treibich-Verdier (DTV) potential, and the Omega background deformed N=2 supersymmetric SU(2) QCD models with four massive flavors in the Nekrasov-Shatashvili limit. The weak coupling spectral solution of the DTV potential is related to the instanton partition function of supersymmetric QCD with surface operator. There are two strong coupling spectral solutions of the DTV potential, they are related to the strong coupling expansions of gauge theory prepotential at the magnetic and dyonic points in the moduli space. A set of duality transformations relate the two strong coupling expansions for spectral solution, and for gauge theory prepotential.

EMBEDDING OF NONCOMMUTATIVE MASSIVE QED

2012 ◽  
Vol 27 (14) ◽  
pp. 1250081 ◽  
Author(s):  
M. MONEMZADEH ◽  
AGHILEH S. EBRAHIMI
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Generating Function ◽  
Gauge Theories ◽  
Chain Structure ◽  
Noncommutative Space ◽  
Class Constraint ◽  
Auxiliary Variables ◽  
Gauge Variation

In this paper, BFT formalism of Proca model in noncommutative space is investigated. Considering that all theories with first class constraint are gauge theories, Proca model in noncommutative space is not a gauge theory in general due to the appearance of second class constraints in it. In present research, the Proca model is converted into a gauge theory using BFT approach by introducing several auxiliary variables which in turn manage to convert the second class constraints to first class ones. Consequently, we apply modified BFT that preserve the chain structure of constraints. Modified BFT has the benefit that it gives less number of independent gauge parameters and we obtain gauge generating function and infinitesimal gauge variation of fields in Proca model. As results, we investigate partition function of this model and embedded noncommutative Proca is ready to quantize in usual way.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals META-STABLE BRANE CONFIGURATIONS WITH MULTIPLE NS5-BRANES

2009 ◽  
Vol 24 (27) ◽  
pp. 5051-5120
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
The Other ◽  
Multiple Product

Starting from an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group and the bifundamentals, we apply Seiberg dual to each gauge group, obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets. Then we describe the intersecting brane configurations, where there are NS-branes and D4-branes (and anti-D4-branes), of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where the orientifold 4-planes are added into the above brane configuration. Next, by adding an orientifold 6-plane, we apply to an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group (where a single symplectic or orthogonal gauge group is present) and the bifundamentals. Finally, we describe the other cases where the orientifold 6-plane intersects with NS-brane.

Renormalization In Quantum Gauge Theory Using Zeta-Function Method

2009 ◽  
Author(s):  
Viorel Chiritoiu ◽  
Gheorghe Zet ◽  
Madalin Bunoiu ◽  
Iosif Malaescu
Keyword(s):  
Gauge Theory ◽  
Zeta Function ◽  
Function Method ◽  
Quantum Gauge Theory

scholarly journals A new generating function for calculating the Igusa local zeta function

2017 ◽  
Vol 304 ◽  
pp. 355-420 ◽  
Author(s):  
Raemeon A. Cowan ◽  
Daniel J. Katz ◽  
Lauren M. White
Keyword(s):  
Zeta Function ◽  
Generating Function ◽  
Local Zeta Function

scholarly journals HAMILTONIAN COHOMOLOGICAL DERIVATION OF FOUR-DIMENSIONAL NONLINEAR GAUGE THEORIES

2002 ◽  
Vol 17 (16) ◽  
pp. 2191-2210 ◽  
Author(s):  
C. BIZDADEA ◽  
E. M. CIOROIANU ◽  
S. O. SALIU
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Gauge Algebra ◽  
Brst Cohomology ◽  
Nonlinear Gauge

Consistent couplings among a set of scalar fields, two types of one-forms and a system of two-forms are investigated in the light of the Hamiltonian BRST cohomology, giving a four-dimensional nonlinear gauge theory. The emerging interactions deform the first-class constraints, the Hamiltonian gauge algebra, as well as the reducibility relations.

SUPERSYMMETRIC TENSOR GAUGE THEORIES

1989 ◽  
Vol 04 (14) ◽  
pp. 1343-1353 ◽  
Author(s):  
T.E. CLARK ◽  
C.-H. LEE ◽  
S.T. LOVE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Sigma Models ◽  
Gauge Field ◽  
Gauge Theories ◽  
Symmetric Tensor ◽  
Global Symmetry ◽  
Invariant Action ◽  
Symmetry Transformations ◽  
Linear Sigma Models

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

scholarly journals MOTIVIC HILBERT ZETA FUNCTIONS OF CURVES ARE RATIONAL

2018 ◽  
Vol 19 (3) ◽  
pp. 947-964
Author(s):  
Dori Bejleri ◽  
Dhruv Ranganathan ◽  
Ravi Vakil
Keyword(s):  
Zeta Function ◽  
Generating Function ◽  
Zeta Functions ◽  
Hilbert Schemes ◽  
Grothendieck Ring

The motivic Hilbert zeta function of a variety $X$ is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points on $X$. In this paper, the motivic Hilbert zeta function of a reduced curve is shown to be rational.

scholarly journals The Riemann Hypothesis is most likely true

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Riemann Hypothesis ◽  
Complex Numbers ◽  
Natural Numbers ◽  
Chebyshev Function ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Sum Of Divisors

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. The Riemann hypothesis belongs to the David Hilbert's list of 23 unsolved problems and it is one of the Clay Mathematics Institute's Millennium Prize Problems. The Robin criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n)< e^{\gamma } \times n \times \log \log n$ holds for all natural numbers $n> 5040$, where $\sigma(x)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. The Nicolas criterion states that the Riemann hypothesis is true if and only if the inequality $\prod_{q \leq q_{n}} \frac{q}{q-1} > e^{\gamma} \times \log\theta(q_{n})$ is satisfied for all primes $q_{n}> 2$, where $\theta(x)$ is the Chebyshev function. Using both inequalities, we show that the Riemann hypothesis is most likely true.

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