scholarly journals Star-triangle type relations from 2d $$ \mathcal{N} $$ = (0, 2) USp(2N) dualities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
J. de-la-Cruz-Moreno ◽  
H. García-Compeán
Keyword(s):  
Dimensional Reduction ◽  
Gauge Theories ◽  
Antisymmetric Tensor ◽  
Tensor Representation ◽  
Type Identity ◽  
First Case ◽  
Relation Type ◽  
Normalization Factors

Abstract Inspired by the gauge/YBE correspondence this paper derives some star-triangle type relations from dualities in 2d$$ \mathcal{N} $$ N = (0, 2) USp(2N) supersymmetric quiver gauge theories. To be precise, we study two cases. The first case is the Intriligator-Pouliot duality in 2d$$ \mathcal{N} $$ N = (0, 2) USp(2N) theories. The description is performed explicitly for N = 1, 2, 3, 4, 5 and also for N = 3k + 2, which generalizes the situation in N = 2, 5. For N = 1 a triangle identity is obtained. For N = 2, 5 it is found that the realization of duality implies slight variations of a star-triangle relation type (STR type). The values N = 3, 4 are associated to a similar version of the asymmetric STR. The second case is a new duality for 2d$$ \mathcal{N} $$ N = (0, 2) USp(2N) theories with matter in the antisymmetric tensor representation that arises from dimensional reduction of 4d$$ \mathcal{N} $$ N = 1 USp(2N) Csáki-Skiba-Schmaltz duality. It is shown that this duality is associated to a triangle type identity for any value of N. In all cases Boltzmann weights as well as interaction and normalization factors are completely determined. Finally, our relations are compared with those previously reported in the literature.

scholarly journals Effective String Description of the Confining Flux Tube at Finite Temperature

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 170
Author(s):  
Michele Caselle
Keyword(s):  
Flux Tube ◽  
Dimensional Reduction ◽  
Conformal Invariance ◽  
Finite Temperature ◽  
Gauge Theories ◽  
Linear Increase ◽  
General Introduction ◽  
Interquark Potential ◽  
Effective String Theory ◽  
Good Agreement

In this review, after a general introduction to the effective string theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement.

scholarly journals Dimensional reduction of gauge theories yielding unified models spontaneously broken to SU3 × U1

1986 ◽  
Vol 263 (3-4) ◽  
pp. 557-590 ◽  
Author(s):  
F.A. Bais ◽  
K.J. Barnes ◽  
P. Forgacs ◽  
G. Zoupanos
Keyword(s):  
Dimensional Reduction ◽  
Gauge Theories

scholarly journals From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories

2021 ◽  
Vol 380 (2216) ◽  
Author(s):  
Uwe-Jens Wiese
Keyword(s):  
Hilbert Space ◽  
Gauge Theory ◽  
Dimensional Reduction ◽  
Gauge Theories ◽  
Quantum Simulation ◽  
Quantum Spin ◽  
Coulomb Phase ◽  
Finite Dimensional ◽  
Link Model ◽  
Quantum Link

Quantum link models provide an extension of Wilson’s lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson’s parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory, these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way ( 1 + 1 ) -d C P ( N − 1 ) models emerge by dimensional reduction from ( 2 + 1 ) -d S U ( N ) quantum spin ladders, the ( 2 + 1 ) -d confining U ( 1 ) gauge theory emerges from the Abelian Coulomb phase of a ( 3 + 1 ) -d quantum link model, and ( 3 + 1 ) -d QCD arises from a non-Abelian Coulomb phase of a ( 4 + 1 ) -d S U ( 3 ) quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories. This article is part of the theme issue ‘Quantum technologies in particle physics’.

scholarly journals Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 856
Author(s):  
George Manolakos ◽  
Pantelis Manousselis ◽  
George Zoupanos
Keyword(s):  
Dimensional Reduction ◽  
Particle Physics ◽  
Extra Dimensions ◽  
Gauge Theories ◽  
Dimensional Theory ◽  
Higher Dimensional ◽  
Coset Spaces ◽  
Gravity Theories ◽  
Physics Model ◽  
Kaluza Klein

First, the Coset Space Dimensional Reduction scheme and the best particle physics model so far resulting from it are reviewed. Then, a higher-dimensional theory in which the extra dimensions are fuzzy coset spaces is described and a dimensional reduction to four-dimensional theory is performed. Afterwards, another scheme including fuzzy extra dimensions is presented, but this time the starting theory is four-dimensional while the fuzzy extra dimensions are generated dynamically. The resulting theory and its particle content is discussed. Besides the particle physics models discussed above, gravity theories as gauge theories are reviewed and then, the whole methodology is modified in the case that the background spacetimes are noncommutative. For this reason, specific covariant fuzzy spaces are introduced and, eventually, the program is written for both the 3-d and 4-d cases.

Some remarks on dimensional reduction of gauge theories and model building

1989 ◽  
Vol 313 (1) ◽  
pp. 95-115 ◽  
Author(s):  
Gerd Rudolph ◽  
Igor P. Volobujev
Keyword(s):  
Dimensional Reduction ◽  
Gauge Theories ◽  
Model Building

scholarly journals GAUGE INVARIANCES IN THE PROCA MODEL

1998 ◽  
Vol 13 (05) ◽  
pp. 765-778 ◽  
Author(s):  
A. S. VYTHEESWARAN
Keyword(s):  
Gauge Theory ◽  
Phase Space ◽  
Projection Operator ◽  
Tensor Field ◽  
Gauge Theories ◽  
Lorentz Invariance ◽  
Maxwell Field ◽  
Antisymmetric Tensor ◽  
Antisymmetric Tensor Field

We show that the Abelian Proca model, which is gauge noninvariant with second class constraints can be converted into gauge theories with first class constraints. The method used, which we call gauge unfixing, employs a projection operator defined in the original phase space. This operator can be constructed in more than one way and so we get more than one gauge theory. Two such gauge theories are the Stückelberg theory and the theory of Maxwell field interacting with an antisymmetric tensor field. We also show that the application of the projection operator does not affect the Lorentz invariance of this model.

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