scholarly journals Undoing decomposition

2019 ◽  
Vol 34 (35) ◽  
pp. 1950233 ◽  
Author(s):  
Eric Sharpe
Keyword(s):  
Sigma Model ◽  
Gauge Theories ◽  
Disjoint Union ◽  
Path Integrals ◽  
Two Dimensions ◽  
Linear Sigma Model ◽  
Two Dimensional ◽  
Yang Mills ◽  
Witten Theory ◽  
Supersymmetric Gauge

In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition — an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov–Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such gaugings explicitly in examples involving orbifolds, nonsupersymmetric pure Yang–Mills theories, and supersymmetric gauge theories in two dimensions. Along the way, we learn explicit concrete details of the topological configurations that path integrals sum over when gauging a one-form symmetry, and we also uncover “hidden” one-form symmetries.

Operator regularization on the hypersphere

1989 ◽  
Vol 67 (7) ◽  
pp. 669-677 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Euclidean Space ◽  
Sigma Model ◽  
Gauge Theories ◽  
Stereographic Projection ◽  
Mass Parameter ◽  
Field Theories ◽  
Dimensional Euclidean Space ◽  
Two Dimensional ◽  
Yang Mills ◽  
Infrared Cutoff

Operator regularization has proved to be a viable way of computing radiative corrections that avoids both the insertion of a regulating parameter into the initial Lagrangian and the occurrence of explicit infinities at any stage of the calculation. We show how this regulating technique can be used in conjunction with field theories defined on an n + 1-dimensional hypersphere, which is the stereographic projection of n-dimensional Euclidean space. The radius of the hypersphere acts as an infrared cutoff, thus eliminating the need to insert a mass parameter to serve as an infrared regulator. This has the advantage of leaving conformai symmetry present in massless theories, intact. We illustrate our approach by considering [Formula: see text], massless Yang–Mills gauge theories and the two-dimensional nonlinear bosonic sigma model with torsion. In the last model, the lowest mode is used as an infrared cutoff.

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 Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

scholarly journals Local G2-manifolds, Higgs bundles and a colored quantum mechanics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Max Hübner
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
View Point ◽  
Yang Mills ◽  
G2 Manifolds ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

scholarly journals On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

scholarly journals ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

2009 ◽  
Vol 24 (32) ◽  
pp. 6105-6121 ◽  
Author(s):  
P. TEOTONIO-SOBRINHO ◽  
C. MOLINA ◽  
N. YOKOMIZO
Keyword(s):  
Hopf Algebras ◽  
Gauge Theories ◽  
Local Symmetry ◽  
Two Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Lattice Field ◽  
Expected Values

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

scholarly journals NONPERTURBATIVE EFFECTIVE ACTIONS OF (N=2)-SUPERSYMMETRIC GAUGE THEORIES

1996 ◽  
Vol 11 (11) ◽  
pp. 1929-1973 ◽  
Author(s):  
A. KLEMM ◽  
W. LERCHE ◽  
S. THEISEN
Keyword(s):  
Riemann Surface ◽  
Effective Action ◽  
Gauge Theories ◽  
Gauge Coupling ◽  
Low Energy ◽  
Yang Mills ◽  
Hyperelliptic Riemann Surface ◽  
Supersymmetric Gauge ◽  
Energy Quantum ◽  
Appell Functions

We elaborate on our previous work on (N=2)-supersymmetric Yang-Mills theory. In particular, we show how to explicitly determine the low energy quantum effective action for G=SU(3) from the underlying hyperelliptic Riemann surface, and calculate the leading instanton corrections. This is done by solving Picard-Fuchs equations and asymptotically evaluating period integrals. We find that the dynamics of the SU(3) theory is governed by an Appell system of type F4, and compute the exact quantum gauge coupling explicitly in terms of Appell functions.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645040
Author(s):  
Arkady Vainshtein
Keyword(s):  
Sigma Models ◽  
Two Dimensions ◽  
Two Dimensional ◽  
World Sheet ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Straightforward Method ◽  
The World ◽  
Original Formula

We study two-dimensional sigma models where the chiral deformation diminished the original [Formula: see text] supersymmetry to the chiral one, [Formula: see text]. Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional [Formula: see text] theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the [Formula: see text] functions in terms of the anomalous dimensions analogous to the NSVZ [Formula: see text] function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

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