scholarly journals Topological operators and completeness of spectrum in discrete gauge theories

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Tom Rudelius ◽  
Shu-Heng Shao
Keyword(s):  
Gauge Theory ◽  
Quantum Gravity ◽  
Global Symmetries ◽  
Gauge Group ◽  
Finite Groups ◽  
Gauge Theories ◽  
Global Symmetry ◽  
Consistent Theory

Abstract In many gauge theories, the existence of particles in every representation of the gauge group (also known as completeness of the spectrum) is equivalent to the absence of one-form global symmetries. However, this relation does not hold, for example, in the gauge theory of non-abelian finite groups. We refine this statement by considering topological operators that are not necessarily associated with any global symmetry. For discrete gauge theory in three spacetime dimensions, we show that completeness of the spectrum is equivalent to the absence of certain Gukov-Witten topological operators. We further extend our analysis to four and higher spacetime dimensions. Since topological operators are natural generalizations of global symmetries, we discuss evidence for their absence in a consistent theory of quantum gravity.

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.

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 Global symmetry, Euclidean gravity, and the black hole information problem

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Daniel Harlow ◽  
Edgar Shaghoulian
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Global Symmetries ◽  
Close Connection ◽  
Usual Sense ◽  
Global Symmetry ◽  
Recent Argument ◽  
Black Hole Information ◽  
Information Problem ◽  
Low Dimensional

Abstract In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity. We also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem in the usual sense, and which therefore can and do have global symmetries. Motivated by this discussion, we conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography.

scholarly journals High energy modular bootstrap, global symmetries and defects

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Sridip Pal ◽  
Zhengdi Sun
Keyword(s):  
Gauge Theory ◽  
Lower Bound ◽  
Global Symmetries ◽  
Topological Defect ◽  
High Energy ◽  
Group Element ◽  
Irreducible Representations ◽  
Global Symmetry ◽  
Modular Invariant ◽  
Scaling Dimension

Abstract We derive Cardy-like formulas for the growth of operators in different sectors of unitary 2 dimensional CFT in the presence of topological defect lines by putting an upper and lower bound on the number of states with scaling dimension in the interval [∆ − δ, ∆ + δ] for large ∆ at fixed δ. Consequently we prove that given any unitary modular invariant 2D CFT symmetric under finite global symmetry G (acting faithfully), all the irreducible representations of G appear in the spectra of the untwisted sector; the growth of states is Cardy like and proportional to the “square” of the dimension of the irrep. In the Schwarzian limit, the result matches onto that of JT gravity with a bulk gauge theory. If the symmetry is non-anomalous, the result applies to any sector twisted by a group element. For c > 1, the statements are true for Virasoro primaries. Furthermore, the results are applicable to large c CFTs. We also extend our results for the continuous U(1) group.

scholarly journals Large N gauge theories with a dense spectrum and the weak gravity conjecture

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Prarit Agarwal ◽  
Jaewon Song
Keyword(s):  
Gauge Theory ◽  
General Theory ◽  
Quantum Gravity ◽  
Gauge Theories ◽  
Degree Of Freedom ◽  
Large N ◽  
The Matrix ◽  
Weak Gravity

Abstract We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional $$ \mathcal{N} $$ N = 1 supersymmetric SU(N) gauge theory with one adjoint and a pair of fundamental/anti-fundamental chiral multiplets. This theory flows to a superconformal theory in the infrared upon a superpotential coupling with gauge singlets. The gap in the low-lying spectrum scales as 1/N and the central charges scale as O(N1) contrary to the usual O(N2) scaling of ordinary gauge theory coming from the matrix degree of freedom. We find the AdS version of the Weak Gravity Conjecture (WGC) holds for this theory, although it cannot be holographically dual to supergravity. This supports the validity of WGC in a more general theory of quantum gravity.

scholarly journals Discrete theta angles, symmetries and anomalies

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Po-Shen Hsin ◽  
Ho Tat Lam
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Topological Quantum Field Theory ◽  
Group Symmetry ◽  
Global Symmetry ◽  
Quantum Field ◽  
Additional Symmetry ◽  
Gauge Groups ◽  
Topological Quantum ◽  
Symmetry Protected

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and ’t Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d4d QCD with SU(N),SU(N)/\mathbb{Z}_kSU(N),SU(N)/ℤk or SO(N)SO(N) gauge groups as well as various 3d3d and 2d2d gauge theories.

scholarly journals The mixed 0-form/1-form anomaly in Hilbert space: pouring the new wine into old bottles

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Andrew A. Cox ◽  
Erich Poppitz ◽  
F. David Wandler
Keyword(s):  
Hilbert Space ◽  
Gauge Group ◽  
Operator Algebra ◽  
Central Extension ◽  
Gauge Theories ◽  
Finite Size ◽  
Background Field ◽  
Symmetry Operator ◽  
Global Symmetry ◽  
Global Center

Abstract We study four-dimensional gauge theories with arbitrary simple gauge group with 1-form global center symmetry and 0-form parity or discrete chiral symmetry. We canonically quantize on 𝕋3, in a fixed background field gauging the 1-form symmetry. We show that the mixed 0-form/1-form ’t Hooft anomaly results in a central extension of the global-symmetry operator algebra. We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite- size torus. We discuss the consistency of these constraints with both older and recent semiclassical calculations in SU(N) theories, with or without adjoint fermions, as well as with their conjectured infrared phases.

The Yang-Mills fields — from the gauge theory to the mechanical model

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Radu Constantinescu ◽  
Carmen Ionescu
Keyword(s):  
Gauge Theory ◽  
Dynamical Systems ◽  
Mechanical Model ◽  
Gauge Theories ◽  
Nonlinear Dynamical Systems ◽  
Gauge Fields ◽  
Global Symmetry ◽  
Nonlinear Dynamical ◽  
Yang Mills ◽  
Mechanical Models

AbstractThe paper presents some mechanical models of gauge theories, i.e. gauge fields transposed in a space with a finite number of degree of freedom. The main focus is on how a global symmetry as the BRST one could be transferred in this context. The mechanical Yang-Mills model modified by taking the ghost type variables into account will be considered as an example of nonlinear dynamical systems.

scholarly journals Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Mendel Nguyen ◽  
Yuya Tanizaki ◽  
Mithat Ünsal
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Lattice Theory ◽  
Lattice Gauge Theory ◽  
Global Symmetry ◽  
Leading Order ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Lattice Gauge ◽  
Abelian Lattice

Abstract We study a 3d lattice gauge theory with gauge group U(1)N−1 ⋊ SN, which is obtained by gauging the SN global symmetry of a pure U(1)N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤN, we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.

scholarly journals Surface defects on E-string from 5-brane webs

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Sung-Soo Kim ◽  
Yuji Sugimoto ◽  
Futoshi Yagi
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Surface Defect ◽  
Gauge Theories ◽  
Surface Defects ◽  
Elliptic Genus ◽  
Partition Functions ◽  
Global Symmetry ◽  
Geometric Transition ◽  
Supersymmetric Gauge

Abstract We study 6d E-string theory with defects on a circle. Our basic strategy is to apply the geometric transition to the supersymmetric gauge theories. First, we calculate the partition functions of the 5d SU(3)0 gauge theory with 10 flavors, which is UV-dual to the 5d Sp(2) gauge theory with 10 flavors, based on two different 5-brane web diagrams, and check that two partition functions agree with each other. Then, by utilizing the geometric transition, we find the surface defect partition function for E-string on ℝ4 × T2. We also discuss that our result is consistent with the elliptic genus. Based on the result, we show how the global symmetry is broken by the defects, and discuss that the breaking pattern depends on where/how we insert the defects.

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