scholarly journals EXACT RESULTS FOR THE SUPERSYMMETRIC G2 GAUGE THEORIES

1995 ◽  
Vol 10 (25) ◽  
pp. 1871-1885 ◽  
Author(s):  
IGOR PESANDO
Keyword(s):  
Fixed Points ◽  
Moduli Space ◽  
Gauge Theories ◽  
Exact Results ◽  
Vector Representation ◽  
Fundamental Vector

We study the N=1 supersymmetric G2 gauge theories with Nf flavors of quarks in the fundamental vector representation. We find dynamically generated superpotentials, smooth quantum moduli space, quantum moduli space with additional mesons, nontrivial ir fixed points.

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 Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

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.

IR fixed points in lattice field theories

2014 ◽  
Vol 29 (25) ◽  
pp. 1445006 ◽  
Author(s):  
L. Del Debbio
Keyword(s):  
Fixed Points ◽  
Predictive Models ◽  
Gauge Theories ◽  
Quantitative Description ◽  
Electroweak Symmetry Breaking ◽  
Field Theories ◽  
Electroweak Symmetry ◽  
Lattice Field ◽  
Starting Point ◽  
Theoretical Foundations

The existence of strongly-interacting infrared (IR) fixed points in gauge theories can be studied using field theories defined on a lattice. Besides their academic interest, it has been argued that these theories could be used as a starting point to construct viable models of electroweak symmetry breaking (EWSB). A quantitative description of the large-distance dynamics is mandatory in order to develop predictive models for phenomenology. In these notes, we discuss the theoretical foundations of IR conformality, and present possible ways to study the problem using the lattice formulation of gauge theories. An overview of current results and methods is discussed.

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