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

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.

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Topological operators and completeness of spectrum in discrete gauge theories

Journal of High Energy Physics ◽

10.1007/jhep12(2020)172 ◽

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.

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Topological terms and anomaly matching in effective field theories on ℝ3 × 𝕊1. Part I. Abelian symmetries and intermediate scales

Journal of High Energy Physics ◽

10.1007/jhep01(2021)091 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Erich Poppitz ◽

F. David Wandler

Keyword(s):

Effective Field Theories ◽

Gauge Theories ◽

Background Field ◽

Effective Field ◽

Field Theories ◽

Global Symmetry ◽

Dirac Fermions ◽

Yang Mills ◽

Local Background ◽

Weyl Fermion

Abstract We explicitly calculate the topological terms that arise in IR effective field theories for SU(N) gauge theories on ℝ3 × 𝕊1 by integrating out all but the lightest modes. We then show how these terms match all global-symmetry ’t Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-U(1) anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chirallagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton ’t Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.

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A composite Higgs with a heavy composite axion

Journal of High Energy Physics ◽

10.1007/jhep12(2020)094 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Tony Gherghetta ◽

Minh D. Nguyen

Keyword(s):

Cp Violation ◽

Gauge Group ◽

Scalar Fields ◽

Higgs Model ◽

Global Symmetry ◽

Color Group ◽

High Scale ◽

Axion Mass ◽

Composite Higgs ◽

The Standard Model

Abstract We consider the strong dynamics associated with a composite Higgs model that simultaneously produces dynamical axions and solves the strong CP problem. The strong dynamics arises from a new Sp or SU(4) hypercolor gauge group containing QCD colored hyperfermions that confines at a high scale. The hypercolor global symmetry is weakly gauged by the Standard Model electroweak gauge group and an enlarged color group, SU(N + 3) × SU(N)′. When hyperfermion condensates form, they not only lead to an SU(5)/SO(5) composite Higgs model but also spontaneously break the enlarged color group to SU(3)c× SU(N)D. At lower energies, the SU(N)D group confines, producing two dynamical axions that eliminates all CP violation. Furthermore, small instantons from the SU(N)′ group can enhance the axion mass, giving rise to TeV scale axion masses that can be detected at collider experiments. Our model provides a way to unify the composite Higgs with dynamical axions, without introducing new elementary scalar fields, while also extending the range of axion masses that addresses the strong CP problem.

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CONFORMAL HOUSE

International Journal of Modern Physics A ◽

10.1142/s0217751x10050391 ◽

2010 ◽

Vol 25 (24) ◽

pp. 4603-4621 ◽

Cited By ~ 20

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.

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META-STABLE BRANE CONFIGURATIONS WITH MULTIPLE NS5-BRANES

International Journal of Modern Physics A ◽

10.1142/s0217751x09045923 ◽

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.

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SUPERSYMMETRIC TENSOR GAUGE THEORIES

Modern Physics Letters A ◽

10.1142/s0217732389001532 ◽

1989 ◽

Vol 04 (14) ◽

pp. 1343-1353 ◽

Cited By ~ 16

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.

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Non-perturbative aspects of Sp(2N) gauge theories

10.23889/suthesis.58291 ◽

2021 ◽

Author(s):

◽

Jack Holligan

Keyword(s):

Gauge Theories ◽

Fine Tuning ◽

Global Symmetry ◽

Dirac Fermions ◽

Open Problems ◽

Abelian Gauge ◽

General Behaviour ◽

Yang Mills ◽

Large N ◽

Glueball Spectrum

Yang-Mills theories based on the symplectic groups – denoted by Sp(2N) – are inter-esting for both theoretical and phenomenological reasons. Sp(2N) theories with two fundamental Dirac fermions give rise to pseudo-Nambu-Goldstone bosons which can be interpreted as a composite Higgs particle. This framework can describe the existing Higgs boson without the need for unnatural ﬁne-tuning. This justiﬁes a programme of wider investigations of Sp(2N) gauge theories aimed at understanding their general behaviour. In this work, we study the glueball mass spectrum for Sp(2N) Yang-Mills theories using the variational method applied to Monte-Carlo generated gauge conﬁg-urations. This is carried out both for ﬁnite N and in the limit N → ∞. The results are compared to existing results for SU(N) Yang-Mills theories, again, for ﬁnite- and large-N. Our glueball analysis is then used to investigate some conjectures related to the behaviour of the spectrum in Yang-Mills theories based on a generic non-Abeliangauge group G. We also ﬁnd numerical evidence that Sp(2N) groups conﬁne both for ﬁnite and large N. As well as studying the glueball spectrum, we examine the quenched-meson spectrum for fermions in the fundamental, antisymmetric and sym-metric representations for N = 2 and N = 3. This study enables us to provide a ﬁrst account of how the related observables vary with N. The investigations presented in this work contribute to our understanding of the non-perturbative dynamics of Sp(2N) gauge theories in connection with Higgs compositeness and, more in general, with fun-damental open problems in non-Abelian gauge theories such as conﬁnement and global symmetry breaking.

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GENERALIZED NONCOMMUTATIVE SUPERALGEBRAS

Modern Physics Letters A ◽

10.1142/s0217732303009551 ◽

2003 ◽

Vol 18 (08) ◽

pp. 587-599 ◽

Cited By ~ 3

Author(s):

REZA ABBASPUR

Keyword(s):

Gauge Symmetry ◽

Gauge Group ◽

Central Extension ◽

Unified Framework ◽

Fermionic Operators ◽

Gauge Connection

Using the notions of gauge symmetry and gauge connection on ordinary superspaces, we derive a class of generalized supertranslation algebras in the case of N = 1, D = 2 Euclidean superspace with a U(1) gauge group. This generalizes the ordinary algebra by inclusion of some additional bosonic and fermionic operators which are interpreted as the generators of the U(1) gauge symmetry on superspace. The generalized superalgebra closes only for very particular configurations of the gauge connection superfield. This provides a unified framework for a variety of generalizations of the ordinary superalgebra such as its central extension and its noncommutative deformation found in an earlier work.

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