Twisted boundary conditions for gauge theories on a torus

1984 ◽  
Vol 25 (9) ◽  
pp. 2736-2740 ◽  
Author(s):  
Alfred Actor
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Twisted Boundary Conditions

scholarly journals Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions

2009 ◽  
Vol 2009 (04) ◽  
pp. 055-055 ◽  
Author(s):  
Hajime Aoki ◽  
Jun Nishimura ◽  
Yoshiaki Susaki
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Matrix Formulation ◽  
Finite Matrix ◽  
Twisted Boundary Conditions

scholarly journals High-order perturbative expansions in massless gauge theories with NSPT

2018 ◽  
Vol 175 ◽  
pp. 11023
Author(s):  
Luigi Del Debbio ◽  
Francesco Di Renzo ◽  
Gianluca Filaci
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Zero Mode ◽  
Stochastic Perturbation ◽  
High Order ◽  
Fundamental Representation ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Twisted Boundary Conditions ◽  
Wilson Fermions

We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degree of freedom. Moreover, the mass of Wilson fermions is affected by an additive renormalisation: we study how to determine the mass counterterms consistently in finite volume. The knowledge of the critical masses will enable high-order perturbative computations in massless QCD, e.g. (as a first application) for the plaquette.

scholarly journals Volume independence for Yang–Mills fields on the twisted torus

2014 ◽  
Vol 29 (25) ◽  
pp. 1445001 ◽  
Author(s):  
Margarita García Pérez ◽  
Antonio González-Arroyo ◽  
Masanori Okawa
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Field Theories ◽  
Gauge Fields ◽  
Dimensional Torus ◽  
Loop Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Twisted Boundary Conditions

We review some recent results related to the notion of volume independence in SU (N) Yang–Mills theories. The topic is discussed in the context of gauge theories living on a d-dimensional torus with twisted boundary conditions. After a brief introduction reviewing the formalism for introducing gauge fields on a torus, we discuss how volume independence arises in perturbation theory. We show how, for appropriately chosen twist tensors, perturbative results to all orders in the 't Hooft coupling depend on a specific combination of the rank of the gauge group (N) and the periods of the torus (l), given by lN2/d, for d even. We discuss the well-known relation to noncommutative field theories and address certain threats to volume independence associated to the occurrence of tachyonic instabilities at one-loop order. We end by presenting some numerical results in 2+1 dimensions that extend these ideas to the nonperturbative domain.

SU(2) and SU(3) gauge theories on a lattice with twisted boundary conditions

1990 ◽  
Vol 334 (1) ◽  
pp. 302-308 ◽  
Author(s):  
I.M. Barbour ◽  
S.J. Psycharis
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Twisted Boundary Conditions

scholarly journals Memory efficient finite volume schemes with twisted boundary conditions

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Eduardo I. Bribián ◽  
Jorge Dasilva Golán ◽  
Margarita García Pérez ◽  
Alberto Ramos
Keyword(s):  
Boundary Conditions ◽  
Finite Volume ◽  
Gauge Theories ◽  
Gradient Flow ◽  
Finite Volume Schemes ◽  
Translational Invariance ◽  
Pure Gauge Theory ◽  
Gpu Clusters ◽  
Twisted Boundary Conditions

AbstractIn this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size $$l^2 \times (Nl)^2$$ l 2 × ( N l ) 2 , a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $$\Lambda $$ Λ parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $$\Lambda _{\overline{\mathrm{MS}}}\sqrt{8 t_0} =0.603(17)$$ Λ MS ¯ 8 t 0 = 0.603 ( 17 ) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals Seiberg-like dualities for orthogonal and symplectic 3d $$ \mathcal{N} $$ = 2 gauge theories with boundaries

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Gauge Groups

Abstract We propose dualities of $$ \mathcal{N} $$ N = (0, 2) supersymmetric boundary conditions for 3d $$ \mathcal{N} $$ N = 2 gauge theories with orthogonal and symplectic gauge groups. We show that the boundary ’t Hooft anomalies and half-indices perfectly match for each pair of the proposed dual boundary conditions.

scholarly journals Entanglement in Finite Quantum Systems Under Twisted Boundary Conditions

2018 ◽  
Vol 48 (5) ◽  
pp. 451-466
Author(s):  
Krissia Zawadzki ◽  
Irene D’Amico ◽  
Luiz N. Oliveira
Keyword(s):  
Boundary Conditions ◽  
Quantum Systems ◽  
Finite Quantum Systems ◽  
Twisted Boundary Conditions
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