scholarly journals A note on instanton counting forN=2 gauge theories with classical gauge groups

2004 ◽  
Vol 2004 (05) ◽  
pp. 021-021 ◽  
Author(s):  
Marcos Marino ◽  
Niclas Wyllard
Keyword(s):  
Gauge Theories ◽  
Gauge Groups

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 A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 393
Author(s):  
Jan F. Haase ◽  
Luca Dellantonio ◽  
Alessio Celi ◽  
Danny Paulson ◽  
Angus Kan ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Gauge Theories ◽  
Hamiltonian Formulation ◽  
Mcmc Methods ◽  
Continuous Limit ◽  
Abelian Gauge ◽  
Gauge Groups

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2+1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

scholarly journals Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups

2013 ◽  
Vol 104 (4) ◽  
pp. 465-493 ◽  
Author(s):  
Francesco Benini ◽  
Richard Eager ◽  
Kentaro Hori ◽  
Yuji Tachikawa
Keyword(s):  
Gauge Theories ◽  
Two Dimensional ◽  
Gauge Groups ◽  
Elliptic Genera ◽  
Rank One

scholarly journals Gauge theories from principally extended disconnected gauge groups

2019 ◽  
Vol 940 ◽  
pp. 351-376 ◽  
Author(s):  
Antoine Bourget ◽  
Alessandro Pini ◽  
Diego Rodríguez-Gómez
Keyword(s):  
Gauge Theories ◽  
Gauge Groups

The cross-over points in lattice gauge theories with continuous gauge groups

1981 ◽  
Vol 105 (2-3) ◽  
pp. 197-200 ◽  
Author(s):  
P. Cvitanović ◽  
J. Greensite ◽  
B. Lautrup
Keyword(s):  
Gauge Theories ◽  
Gauge Groups ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
The Cross

scholarly journals A string theory realization of special unitary quivers in 3 dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andrés Collinucci ◽  
Roberto Valandro
Keyword(s):  
String Theory ◽  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Holomorphic Curves ◽  
Gauge Groups ◽  
Unitary Gauge

Abstract We propose a string theory realization of three-dimensional $$ \mathcal{N} $$ N = 4 quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in local K3’s, by invoking the Stückelberg mechanism. From the type IIB perspective, this is understood as simply compactifying the familiar Hanany-Witten (HW) constructions on a T3. The mirror symmetry duals are easily derived. We illustrate this with various examples of mirror pairs.

scholarly journals Finite-N corrections to the superconformal index of toric quiver gauge theories

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Reona Arai ◽  
Shota Fujiwara ◽  
Yosuke Imamura ◽  
Tatsuya Mori
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Gauge Groups ◽  
Superconformal Index

Abstract The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi–Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite-$N$ corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small sizes of gauge groups, and confirm that the formula correctly reproduces the finite-$N$ corrections up to the expected order.

scholarly journals Discrete gauging and Hasse diagrams

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Guillermo Arias Tamargo ◽  
Antoine Bourget ◽  
Alessandro Pini
Keyword(s):  
Gauge Theories ◽  
Hilbert Series ◽  
Higgs Mechanism ◽  
Coulomb Branch ◽  
Gauge Groups ◽  
Hasse Diagrams

We analyse the Higgs branch of 4d \mathcal{N}=2𝒩=2 SQCD gauge theories with non-connected gauge groups \widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2SŨ(N)=SU(N)⋊I,IIℤ2 whose study was initiated in . We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d \mathcal{N}=4𝒩=4 magnetic quivers for the Higgs branches in the type II discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.

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.

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