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 Higgsing towards E-strings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Kimyeong Lee
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
The Self ◽  
Flavor Symmetry ◽  
Strongly Coupled ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Elliptic Genera ◽  
Linear Sigma Models

Abstract We explore 6d (1, 0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an E8 wall. Specifically, we study the 2d $$ \mathcal{N} $$ N = (0, 4) gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0, 4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the E8 wall, and find their fully refined elliptic genera.

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 PHASE TRANSITION COUPLINGS IN U(1) and SU(N) REGULARIZED GAUGE THEORIES

2001 ◽  
Vol 16 (24) ◽  
pp. 3989-4009 ◽  
Author(s):  
L. V. LAPERASHVILI ◽  
D. A. RYZHIKH ◽  
H. B. NIELSEN
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Gauge Theories ◽  
Planck Scale ◽  
Structure Constant ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Multiple Point ◽  
Yang Mills ◽  
Loop Approximation

Using a two-loop approximation for β functions, we have considered the corresponding renormalization group improved effective potential in the dual Abelian Higgs model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU (N) regularized gauge theories. In contrast to our previous result α crit ≈0.17, obtained in the one-loop approximation with the DAHM effective potential (see Ref. 20), the critical value of the electric fine structure constant in the two-loop approximation, calculated in the present paper, is equal to α crit ≈0.208 and coincides with the lattice result for compact QED10: [Formula: see text]. Following the 't Hooft's idea of the "Abelization" of monopole vacuum in the Yang–Mills theories, we have obtained an estimation of the SU (N) triple point coupling constants, which is [Formula: see text]. This relation was used for the description of the Planck scale values of the inverse running constants [Formula: see text] (i= 1, 2, 3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the multiple point model.16

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.

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 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 Fradkin–Shenker continuity and “instead-of-confinement” phase

2017 ◽  
Vol 32 (30) ◽  
pp. 1750159 ◽  
Author(s):  
M. Shifman ◽  
A. Yung
Keyword(s):  
Phase Transition ◽  
Weak Coupling ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Fundamental Representation ◽  
Quark Confinement ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Confinement Phase

In 1979, Fradkin and Shenker observed [Phys. Rev. D 19, 3682 (1979)] that if one considers a Yang–Mills theory fully Higgsed by virtue of scalar fields in the fundamental representation of the SU(N) gauge group there is no phase transition in passing from the Higgs regime (weak coupling) to the “QCD confinement” regime at strong coupling. The above two regimes are continuously connected. We combine this observations with lessons from supersymmetric gauge theories which show that the Higgs phase is continuously connected to what is called “instead-of-confinement” phase rather than the phase with quark confinement. In the “instead-of-confinement” phase monopoles are confined and play a role of “constituent” quarks inside hadrons. In contrast, the Seiberg–Witten phase of quark confinement is not analytically connected to the Higgs phase. We propose dedicated lattice studies of Yang–Mills theories with scalar quarks.

scholarly journals Supersymmetry breaking deformations and phase transitions in five dimensions

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Matteo Bertolini ◽  
Francesco Mignosa
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Phase Transitions ◽  
Supersymmetry Breaking ◽  
Gauge Coupling ◽  
Global Symmetry ◽  
Five Dimensions ◽  
Yang Mills ◽  
New Phase ◽  
Mass Deformation

Abstract We analyze a recently proposed supersymmetry breaking mass deformation of the E1 superconformal fixed point in five dimensions which, at weak gauge coupling, leads to pure SU(2) Yang-Mills and which was conjectured to lead to an interacting CFT at strong coupling. We provide an explicit geometric construction of the deformation using brane-web techniques and show that for large enough gauge coupling a global symmetry is spontaneously broken and the theory enters a new phase which, at infinite coupling, displays an instability. The Yang-Mills and the symmetry broken phases are separated by a phase transition. Depending on the structure of the potential, this can be first or second order.

scholarly journals Time-reversal symmetry, anomalies, and dualities in (2+1)$d$

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Clay Cordova ◽  
Po-Shen Hsin ◽  
Nathan Seiberg
Keyword(s):  
Time Reversal ◽  
Gauge Theories ◽  
Dirac Fermion ◽  
Global Symmetry ◽  
Time Reversal Symmetry ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Long Distance ◽  
Free Theory ◽  
Topological Quantum

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry \cal T. The standard relation {\cal T}^2=(-1)^F is satisfied on all the “perturbative operators” i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators {\cal T}^2=(-1)^F {\cal M} with \cal M a non-trivial global symmetry. For example, acting on monopole operators, \cal M could be \pm1±1 depending on the magnetic charge. We study in detail U(1)U(1) gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is 2 ~{\rm mod }~4, e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge 22 is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to SO(N)SO(N) gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.

scholarly journals PHASE TRANSITION IN GAUGE THEORIES, MONOPOLES AND THE MULTIPLE POINT PRINCIPLE

2005 ◽  
Vol 20 (26) ◽  
pp. 5911-5988 ◽  
Author(s):  
C. R. DAS ◽  
L. V. LAPERASHVILI
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Gauge Theories ◽  
Magnetic Charge ◽  
Coupling Constants ◽  
Asymptotic Freedom ◽  
Multiple Point ◽  
Group Model ◽  
Loop Approximation ◽  
Renormalization Group Equations

This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Using renormalization group equations for the SM, the effective potential in the two-loop approximation is investigated, and the existence of its postulated second minimum at the fundamental scale is confirmed. Phase transitions in the lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs monopole model, in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with magnetic charge. Considering our (3+1)-dimensional space–time as, in some way, discrete or imagining it as a lattice with a parameter a = λP, where λP is the Planck length, we have investigated the additional contributions of monopoles to the β-functions of renormalization group equations for running fine structure constants αi(μ) (i = 1, 2, 3 correspond to the U (1), SU(2) and SU(3) gauge groups of the SM) in the FRGGM extended beyond the SM at high energies. It is shown that monopoles have N fam times smaller magnetic charge in the FRGGM than in the SM (N fam is a number of families in the FRGGM). We have estimated also the enlargement of a number of fermions in the FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have reviewed that, in contrast to the case of the Anti-grand-unified-theory (AGUT), there exists a possibility of unification of all gauge interactions (including gravity) near the Planck scale due to monopoles. The possibility of the [SU(5)]3 or [SO(10)]3 unification at the GUT-scale ~1018 GeV is briefly considered.

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