scholarly journals Classification of large N superconformal gauge theories with a dense spectrum

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Prarit Agarwal ◽  
Ki-Hong Lee ◽  
Jaewon Song
Keyword(s):  
Gauge Theories ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Matter Content ◽  
Gauge Groups ◽  
Weakly Coupled ◽  
Large N ◽  
The Difference ◽  
Supersymmetric Gauge

Abstract We classify the large N limits of four-dimensional supersymmetric gauge theories with simple gauge groups that flow to superconformal fixed points. We restrict ourselves to the ones without a superpotential and with a fixed flavor symmetry. We find 35 classes in total, with 8 having a dense spectrum of chiral gauge-invariant operators. The central charges a and c for the dense theories grow linearly in N in contrast to the N2 growth for the theories with a sparse spectrum. The difference between the central charges a − c can have both signs, and it does not vanish in the large N limit for the dense theories. We find that there can be multiple bands separated by a gap, or a discrete spectrum above the band. We also find a criterion on the matter content for the fixed point theory to possess either a dense or sparse spectrum. We discover a few curious aspects regarding supersymmetric RG flows and a-maximization along the way. For all the theories with the dense spectrum, the AdS version of the Weak Gravity Conjecture (including the convex hull condition for the cases with multiple U(1)’s) holds for large enough N even though they do not have weakly-coupled gravity duals.

scholarly journals β-functions in large-N supersymmetric gauge theories

1997 ◽  
Vol 504 (1-2) ◽  
pp. 108-126 ◽  
Author(s):  
PM. Ferreira ◽  
I. Jack ◽  
D.R.T. Jones ◽  
C.G. North
Keyword(s):  
Gauge Theories ◽  
Supersymmetric Gauge Theories ◽  
Large N ◽  
Supersymmetric Gauge

scholarly journals The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories

2004 ◽  
Vol 8 (4) ◽  
pp. 603-696 ◽  
Author(s):  
Ofer Aharony ◽  
Joseph Marsano ◽  
Shiraz Minwalla ◽  
Kyriakos Papadodimas ◽  
Mark Van Raamsdonk
Keyword(s):  
Phase Transition ◽  
Gauge Theories ◽  
Weakly Coupled ◽  
Large N ◽  
Deconfinement Phase Transition

scholarly journals Higher-form symmetries of 6d and 5d theories

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Lakshya Bhardwaj ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Matter Content ◽  
Gauge Fields ◽  
Symmetry Groups ◽  
Abelian Gauge ◽  
Superconformal Field Theories ◽  
Supersymmetric Gauge ◽  
Web Construction

Abstract We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

QCD AND SUPERSYMMETRY

2010 ◽  
Vol 25 (02n03) ◽  
pp. 470-489
Author(s):  
ADI ARMONI
Keyword(s):  
Gauge Theories ◽  
Quark Condensate ◽  
Supersymmetric Gauge Theories ◽  
Yang Mills ◽  
The Third ◽  
Large N ◽  
Supersymmetric Gauge ◽  
Supersymmetric Theories ◽  
Theory Formula

We review the connection between QCD and supersymmetric theories. We focus on the non-perturbative large- N (planar) correspondence between one-flavor QCD and pure supersymmetric Yang-Mills theory ([Formula: see text]). We explain how non-perturbative quantities in QCD, such as the quark condensate, can be evaluated by using the corresponding non-perturbative results in supersymmetric gauge theories. The review consists of three parts. The first part is devoted to a review of pure [Formula: see text]. In the second part we introduce "orientifold planar equivalence". The third part is devoted to the implications of planar equivalence for QCD.

scholarly journals META-STABLE BRANE CONFIGURATIONS BY DUALIZING THE TWO GAUGE GROUPS

2010 ◽  
Vol 25 (06) ◽  
pp. 1185-1210
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Meson Field ◽  
Supersymmetric Gauge Theories ◽  
Gauge Groups ◽  
Interaction Term ◽  
Mass Terms ◽  
Supersymmetric Gauge ◽  
Electric Theory

We consider the [Formula: see text] supersymmetric gauge theories with product gauge groups. The two kinds of D6-branes in the electric theory are both displaced and rotated respectively where these deformations are interpreted as the mass terms and quartic terms for the two kinds of flavors. Then we apply the Seiberg dual to the whole gauge group factors by moving the branes and obtain the corresponding dual gauge theories. By analyzing the magnetic superpotentials consisting of an interaction term between a magnetic meson field and dual matters as well as the above deformations for each gauge group, we present the type IIA nonsupersymmetric meta-stable brane configurations.

Elements of Geometry of Balls in Banach Spaces

2018 ◽  
Author(s):  
Kazimierz Goebel ◽  
Stanislaw Prus
Keyword(s):  
Functional Analysis ◽  
Graduate Students ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Normed Spaces ◽  
The Subject ◽  
Basic Facts ◽  
Weak Topologies

One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects contains: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory, and others. The aim of this book is to present basic facts from this field. It is addressed to advanced undergraduate and graduate students interested in the subject. For some it may result in further interest, a continuation and deepening of their study of the subject. It may be also useful for instructors running courses on functional analysis, supervising diploma theses or essays on various levels.

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