scholarly journals Vector fields, RG flows and emergent gauge symmetry

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Daniel Nogradi
Keyword(s):  
Phase Diagram ◽  
Gauge Symmetry ◽  
Fixed Points ◽  
Vector Fields ◽  
Gauge Theories ◽  
The Other ◽  
Rich Phase ◽  
Four Dimensions ◽  
Yang Mills ◽  
Renormalizable Theory

Abstract We consider the most general perturbatively renormalizable theory of vector fields in four dimensions with a global SU(N) symmetry and massless couplings. The Lagrangian contains 1 quadratic, 2 cubic and 4 quartic couplings. The RG flow among this set of 7 couplings is computed to 1-loop and a rich phase diagram is mapped out; in particular it is shown that a finite number of asymptotically free RG-flows exist corresponding to non-trivial fixed points for the ratios of the couplings. None of these are gauge theories, i.e. possess only global SU(N) invariance but not a local one. We also include the most general ghost couplings, still with global SU(N) invariance, and compute the RG flow to 1-loop for all 9 resulting couplings. Again asymptotically free RG flows exist with non-trivial fixed points for the ratios of couplings. It is shown that Yang-Mills theory emerges at a particular fixed point. The theories at the other fixed points are marginally relevant gauge symmetry violating perturbations of Yang-Mills theory. The large-N limit is also investigated in detail.

scholarly journals Two-loop rational terms in Yang-Mills theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jean-Nicolas Lang ◽  
Stefano Pozzorini ◽  
Hantian Zhang ◽  
Max F. Zoller
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Theories ◽  
A Posteriori ◽  
Four Dimensions ◽  
Yang Mills ◽  
General Properties ◽  
Finite Set ◽  
Numerical Tools ◽  
Loop Amplitudes

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

scholarly journals ANTI-DE SITTER SPACE, THERMAL PHASE TRANSITION AND CONFINEMENT IN GAUGE THEORIES

2001 ◽  
Vol 16 (16) ◽  
pp. 2747-2769 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Gauge Theories ◽  
De Sitter Space ◽  
Spontaneous Breaking ◽  
De Sitter ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Classical Geometry ◽  
Large N ◽  
Quantum Phenomena

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

scholarly journals R Symmetry and the Topological Twist of N = 2 Effective Supergravities of Heterotic Strings

1997 ◽  
Vol 12 (02) ◽  
pp. 379-418 ◽  
Author(s):  
Marco Billó ◽  
Pietro Fré ◽  
Riccardo D'auria ◽  
Sergio Ferrara ◽  
Paolo Soriani ◽  
...  
Keyword(s):  
Gauge Theories ◽  
The Other ◽  
Tree Level ◽  
Vector Multiplet ◽  
Continuous Symmetry ◽  
Yang Mills ◽  
Heterotic Strings ◽  
Axion Field ◽  
Effective Theories ◽  
R Symmetry

We discuss R symmetries in locally supersymmetric N = 2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton–axion field has different R charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang–Mills instantons with triholomorphic hyperinstantons and axion instantons. For the tree level classical special manifolds ST(n) = SU(1,1)/U(1) × SO(2,n)/[SO(2) × SO(n)], R symmetry with the specified properties is a continuous symmetry, but for the quantum-corrected manifolds [Formula: see text] a discrete R group of electric–magnetic duality rotations is sufficient and we argue that it exists.

scholarly journals Constrained gauge-gravity duality in three and four dimensions

2020 ◽  
Vol 80 (1) ◽  
Author(s):  
T. S. Assimos ◽  
R. F. Sobreiro
Keyword(s):  
Gauge Symmetry ◽  
Geometric Constraints ◽  
Three Dimensions ◽  
Nucl Phys ◽  
Bundle Theory ◽  
De Sitter ◽  
Four Dimensions ◽  
Yang Mills ◽  
Set Up ◽  
Gauge Gravity

AbstractThe equivalence between Chern–Simons and Einstein–Hilbert actions in three dimensions established by Achúcarro and Townsend (Phys Lett B 180:89, 1986) and Witten (Nucl Phys B 311:46, 1988) is generalized to the off-shell case. The technique is also generalized to the Yang–Mills action in four dimensions displaying de Sitter gauge symmetry. It is shown that, in both cases, we can directly identify a gravity action while the gauge symmetry can generate spacetime local isometries as well as diffeomorphisms. The price we pay for working in an off-shell scenario is that specific geometric constraints are needed. These constraints can be identified with foliations of spacetime. The special case of spacelike leafs evolving in time is studied. Finally, the whole set up is analyzed under fiber bundle theory. In this analysis we show that a traditional gauge theory, where the gauge field does not influence in spacetime dynamics, can be (for specific cases) consistently mapped into a gravity theory in the first order formalism.

scholarly journals Electron Liquid in Double-layer Structures

1993 ◽  
Vol 46 (3) ◽  
pp. 423 ◽  
Author(s):  
L Swierkowski ◽  
D Neilson ◽  
J Szymanski
Keyword(s):  
Phase Diagram ◽  
Gallium Arsenide ◽  
Liquid Phase ◽  
Excitation Spectrum ◽  
Coulomb Interaction ◽  
The Other ◽  
Many Body ◽  
Rich Phase ◽  
Layer Structures ◽  
Uniform Liquid

Two layers of electrons or holes trapped at the adjacent interfaces of a gallium arsenide heterostructure can interact through the Coulomb interaction; this leads to a rich phase diagram of ground states, some of which are inhomogeneous in density. The cause of this is associated with each layer's acting as a polarisable background for the other, making it much easier for inhomogeneous configurations to be stable. Even in the uniform liquid phase the presence of a second layer can qualitatively change the nature of the low lying excitation spectrum and lead to large many-body effects in the spectrum, even at very long wavelengths.

scholarly journals DEFORMED SUPERSYMMETRIC GAUGE THEORIES FROM THE FLUXTRAP BACKGROUND

2013 ◽  
Vol 28 (28) ◽  
pp. 1330044 ◽  
Author(s):  
DOMENICO ORLANDO ◽  
SUSANNE REFFERT
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
Recent Literature ◽  
Supersymmetric Gauge Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
M Theory ◽  
Super Yang Mills Theory ◽  
Gravity Duals

The fluxtrap background of string theory provides a transparent and algorithmic way of constructing supersymmetric gauge theories with both mass and Ω-type deformations in various dimensions. In this paper, we review a number of deformed supersymmetric gauge theories in two and four dimensions which can be obtained via the fluxtrap background from string or M-theory. Such theories, the most well-known being Ω-deformed super-Yang–Mills theory in four dimensions, have met with a lot of interest in the recent literature. The string theory treatment offers many new avenues of analysis and applications, such as for example the study of the gravity duals for deformed [Formula: see text] gauge theories.

scholarly journals Quiver Gauge Theories: Finitude and Trichotomoty

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 291
Author(s):  
Yang-Hui He
Keyword(s):  
Gauge Theories ◽  
Beta Function ◽  
Asymptotic Freedom ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Four Dimensions ◽  
Yang Mills ◽  
Path Algebras ◽  
Representation Types ◽  
Standard Techniques

D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of standard techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, conformality and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then, we utilise certain results from graph theory and axiomatic representation theory of path algebras to address physical issues such as the implication of graph additivity to finiteness of gauge theories, the impossibility of constructing completely IR free string orbifold theories and the unclassifiability of N < 2 Yang-Mills theories in four dimensions.

CONSISTENT QUANTIZATION OF A CHIRAL GAUGE THEORY IN FOUR DIMENSIONS

1989 ◽  
Vol 04 (27) ◽  
pp. 2675-2683 ◽  
Author(s):  
SHOGO MIYAKE ◽  
KEN-ICHI SHIZUYA
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Gauge Field ◽  
Current Algebra ◽  
Gauge Theories ◽  
Present Theory ◽  
Particle Spectrum ◽  
Four Dimensions ◽  
Symmetric Formulation

Using a gauge-symmetric formulation of anomalous gauge theories, we study the consistency and symmetry contents of a chiral gauge theory in four dimensions. The gauge symmetry, restored by the inclusion of the Wess-Zumino term, is spontaneously broken and the gauge field acquires a mass. Symmetry arguments are used to determine the particle spectrum and the current algebra of the model. Our analysis indicates that, apart from a question of renormalizability, the present theory is a consistent gauge 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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