scholarly journals Instantons, symmetries and anomalies in five dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Luigi Tizzano
Keyword(s):  
Fixed Points ◽  
Gauge Theories ◽  
Global Symmetry ◽  
Flavor Symmetry ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Fundamental Matter ◽  
Dynamical Properties ◽  
Supersymmetric Gauge ◽  
Classical Background

Abstract All five-dimensional non-abelian gauge theories have a U(1)I global symmetry associated with instantonic particles. We describe an obstruction to coupling U(1)I to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed ’t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.

scholarly journals The Cat’s Cradle: deforming the higher rank E1 and $$ {\tilde{E}}_1 $$ theories

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Oren Bergman ◽  
Diego Rodríguez-Gómez
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Global Symmetry ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Higher Rank ◽  
Supersymmetric Gauge

Abstract We use 5-brane webs to study the two-dimensional space of supersymmetric mass deformations of higher rank generalizations of the 5d E1 and $$ {\tilde{E}}_1 $$ E ˜ 1 theories. Some of the resulting IR phases are described by IR free supersymmetric gauge theories, while others correspond to interacting fixed points. The number of different phases appears to grow with the rank. The space of deformations is qualitatively different for the even and odd rank cases, but that of the even (odd) rank E1 theory is similar to that of the odd (even) rank $$ {\tilde{E}}_1 $$ E ˜ 1 theory. One result of our analysis predicts that the supersymmetric SU(N) theory with CS level k = $$ \frac{N}{2} $$ N 2 + 4 and a single massless antisymmetric hypermultiplet exhibits an enhanced global symmetry at the UV fixed point, given by SU(2) × SU(2) if N is even, and SU(2) × U(1) if N is odd.

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

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.

scholarly journals Non-invertible global symmetries and completeness of the spectrum

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Ben Heidenreich ◽  
Jacob McNamara ◽  
Miguel Montero ◽  
Matthew Reece ◽  
Tom Rudelius ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Cosmic Strings ◽  
Global Symmetry ◽  
Complete Spectrum ◽  
Abelian Gauge ◽  
Analogous Statement ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Chern Simons ◽  
General Gauge

Abstract It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

scholarly journals Anomalies in the space of coupling constants and their dynamical applications II

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Clay Cordova ◽  
Daniel Freed ◽  
Ho Tat Lam ◽  
Nathan Seiberg
Keyword(s):  
Phase Transitions ◽  
Time Reversal ◽  
Discrete Symmetries ◽  
Gauge Theories ◽  
Coupling Constants ◽  
Global Symmetry ◽  
Flavor Symmetry ◽  
Fundamental Representation ◽  
Yang Mills ◽  
Simply Connected

We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form global symmetry (associated with the center) and the periodicity of the \thetaθ-parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as time-reversal). We also study SU(N)SU(N) and Sp(N)Sp(N) gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the \thetaθ-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.

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.

scholarly journals Topological aspects of 4D Abelian lattice gauge theories with the θ parameter

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Masazumi Honda ◽  
Yuya Tanizaki
Keyword(s):  
Phase Diagram ◽  
Gauge Theories ◽  
Global Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Self Duality ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
The Rich ◽  
Abelian Lattice

Abstract We study a four-dimensional U(1) gauge theory with the θ angle, which was originally proposed by Cardy and Rabinovici. It is known that the model has the rich phase diagram thanks to the presence of both electrically and magnetically charged particles. We discuss the topological nature of the oblique confinement phase of the model at θ = π, and show how its appearance can be consistent with the anomaly constraint. We also construct the SL(2, ℤ) self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry. This self-duality has a mixed ’t Hooft anomaly with gravity, and its implications on the phase diagram is uncovered. As the model shares the same global symmetry and ’t Hooft anomaly with those of SU(N) Yang-Mills theory, studying its topological aspects would provide us more hints to explore possible dynamics of non-Abelian gauge theories with nonzero θ angles.

scholarly journals Thermal order in large N conformal gauge theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Soumyadeep Chaudhuri ◽  
Changha Choi ◽  
Eliezer Rabinovici
Keyword(s):  
Symmetry Breaking ◽  
Fixed Points ◽  
Gauge Theories ◽  
Scalar Fields ◽  
The Other ◽  
Spontaneous Breaking ◽  
Global Symmetry ◽  
Gauge Groups ◽  
Large N ◽  
Work Done

Abstract In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in D = 4 space-time dimensions. We show that such a symmetry-breaking indeed occurs in certain families of non-supersymmetric large N gauge theories at a planar limit. We also show that this phenomenon is accompanied by the system remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature. These analyses are motivated by the work done in [1, 2] where symmetry-breaking was observed in all thermal states for certain CFTs in fractional dimensions.In our case, the theories demonstrating the above features have gauge groups which are specific products of SO(N) in one family and SU(N) in the other. Working in a perturbative regime at the N → ∞ limit, we show that the beta functions in these theories yield circles of fixed points in the space of couplings. We explicitly check this structure up to two loops and then present a proof of its survival under all loop corrections. We show that under certain conditions, an interval on this circle of fixed points demonstrates both the spontaneous breaking of a global symmetry as well as a persistent BEH phase at all nonzero temperatures. The broken global symmetry is ℤ2 in one family of theories and U(1) in the other. The corresponding order parameters are expectation values of the determinants of bifundamental scalar fields in these theories. We characterize these symmetries as baryon-like symmetries in the respective models.

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