scholarly journals Surface operators, chiral rings and localization in N $$ \mathcal{N} $$ =2 gauge theories

2017 ◽  
Vol 2017 (11) ◽  
Author(s):  
S. K. Ashok ◽  
M. Billò ◽  
E. Dell’Aquila ◽  
M. Frau ◽  
V. Gupta ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Chiral Rings

scholarly journals Chiral rings and phases of supersymmetric gauge theories

2003 ◽  
Vol 2003 (04) ◽  
pp. 018-018 ◽  
Author(s):  
Freddy Cachazo ◽  
Nathan Seiberg ◽  
Edward Witten
Keyword(s):  
Gauge Theories ◽  
Supersymmetric Gauge Theories ◽  
Chiral Rings ◽  
Supersymmetric Gauge

scholarly journals Chiral Rings, Superpotentials and the Vacuum Structure of N = 1 Supersymmetric Gauge Theories

2003 ◽  
Vol 7 (2) ◽  
pp. 269-305 ◽  
Author(s):  
Andreas Brandhuber ◽  
Harald Ita ◽  
Harald Nieder ◽  
Yaron Oz ◽  
Christian Romelsberger
Keyword(s):  
Gauge Theories ◽  
Supersymmetric Gauge Theories ◽  
Vacuum Structure ◽  
Chiral Rings ◽  
Supersymmetric Gauge

scholarly journals Chiral rings, Futaki invariants, plethystics, and Gröbner bases

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jiakang Bao ◽  
Yang-Hui He ◽  
Yan Xiao
Keyword(s):  
Moduli Spaces ◽  
Gauge Theories ◽  
Hilbert Series ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Complete Intersections ◽  
Grobner Basis ◽  
Supersymmetric Gauge Theories ◽  
Chiral Rings ◽  
Supersymmetric Gauge

Abstract We study chiral rings of 4d $$ \mathcal{N} $$ N = 1 supersymmetric gauge theories via the notion of K-stability. We show that when using Hilbert series to perform the computations of Futaki invariants, it is not enough to only include the test symmetry information in the former’s denominator. We discuss a way to modify the numerator so that K-stability can be correctly determined, and a rescaling method is also applied to simplify the calculations involving test configurations. All of these are illustrated with a host of examples, by considering vacuum moduli spaces of various theories. Using Gröbner basis and plethystic techniques, many non-complete intersections can also be addressed, thus expanding the list of known theories in the literature.

scholarly journals Boundaries, Vermas and factorisation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Mathew Bullimore ◽  
Samuel Crew ◽  
Daniel Zhang
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Building Blocks ◽  
Partition Functions ◽  
Verma Modules ◽  
Coulomb Branch ◽  
Superconformal Index ◽  
Chiral Rings ◽  
Real Mass

Abstract We revisit the factorisation of supersymmetric partition functions of 3d $$ \mathcal{N} $$ N = 4 gauge theories. The building blocks are hemisphere partition functions of a class of UV $$ \mathcal{N} $$ N = (2, 2) boundary conditions that mimic the presence of isolated vacua at infinity in the presence of real mass and FI parameters. These building blocks can be unambiguously defined and computed using supersymmetric localisation. We show that certain limits of these hemisphere partition functions coincide with characters of lowest weight Verma mod- ules over the quantised Higgs and Coulomb branch chiral rings. This leads to expressions for the superconformal index, twisted index and S3 partition function in terms of such characters. On the way we uncover new connections between boundary ’t Hooft anomalies, hemisphere partition functions and lowest weights of Verma modules.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

Path integral for gauge theories with fermions

1980 ◽  
Vol 21 (10) ◽  
pp. 2848-2858 ◽  
Author(s):  
Kazuo Fujikawa
Keyword(s):  
Path Integral ◽  
Gauge Theories
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