scholarly journals Dualities for three-dimensional $$ \mathcal{N} $$ = 2 SU(Nc) chiral adjoint SQCD

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Antonio Amariti ◽  
Marco Fazzi
Keyword(s):  
Three Dimensional ◽  
Complete Classification ◽  
Previous Literature ◽  
Partition Functions ◽  
Three Sphere ◽  
Chern Simons

Abstract We study dualities for 3d $$ \mathcal{N} $$ N = 2 SU(Nc) SQCD at Chern-Simons level k in presence of an adjoint with polynomial superpotential. The dualities are dubbed chiral because there is a different amount of fundamentals Nf and antifundamentals Na. We build a complete classification of such dualities in terms of |Nf− Na| and k. The classification is obtained by studying the flow from the non-chiral case, and we corroborate our proposals by matching the three-sphere partition functions. Finally, we revisit the case of SU(Nc) SQCD without the adjoint, comparing our results with previous literature.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

Classification of 3-dimensional left-invariant almost paracontact metric structures

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Complete Classification ◽  
Natural Assumption ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

scholarly journals Constant mean curvature spheres in homogeneous three-manifolds

2020 ◽  
Author(s):  
William H. Meeks ◽  
Pablo Mira ◽  
Joaquín Pérez ◽  
Antonio Ros
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Three Dimensional ◽  
Complete Classification ◽  
Homogeneous Manifolds ◽  
The Mean

Abstract We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.

scholarly journals Exact results and Schur expansions in quiver Chern-Simons-matter theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Leonardo Santilli ◽  
Miguel Tierz
Keyword(s):  
Simons Theory ◽  
Partition Functions ◽  
Wilson Loops ◽  
Model Formulation ◽  
Schur Polynomials ◽  
Three Sphere ◽  
The Matrix ◽  
The Masses ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters tj = −e2πmj , where mj are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.

scholarly journals Lie symmetries and singularity analysis for generalized shallow-water equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 739-747
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Singularity Analysis ◽  
Complete Classification ◽  
Similarity Solutions ◽  
Lie Symmetries ◽  
Reduced Equations ◽  
Complete Study ◽  
The One

AbstractWe perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm (CH) equation and the generalized Benjamin-Bono-Mahoney (BBM) equation. From the Lie theory we find that the two equations are invariant under the same three-dimensional Lie algebra which is the same Lie algebra admitted by the CH equation. We determine the one-dimensional optimal system for the admitted Lie symmetries and we perform a complete classification of the similarity solutions for the two equations of our study. The reduced equations are studied by using the point symmetries or the singularity analysis. Finally, the singularity analysis is directly applied on the partial differential equations from where we infer that the generalized equations of our study pass the singularity test and are integrable.

The complete classification of a class of conformally flat Lorentzian hypersurfaces in ℝ14

2017 ◽  
Vol 28 (13) ◽  
pp. 1750092
Author(s):  
Zhenxiao Xie ◽  
Changping Wang ◽  
Xiaozhen Wang
Keyword(s):  
Three Dimensional ◽  
Complete Classification ◽  
Conformally Flat ◽  
Space Forms ◽  
Lorentzian Space ◽  
Lorentzian Metric ◽  
Cone Model ◽  
Shape Operators ◽  
Frenet Curves

A three-dimensional Lorentzian hypersurface [Formula: see text] is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of [Formula: see text]. In this paper, using the projective light-cone model, we give a complete classification of those ones whose shape operators have two distinct real eigenvalues and cannot be diagonalizable. These hypersurfaces are conformal equivalent to cones, cylinders, or rotational hypersurfaces generated by B-scrolls (over null Frenet curves) in three-dimensional Lorentzian space forms.

scholarly journals Higher-derivative supergravity, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Nikolay Bobev ◽  
Anthony M. Charles ◽  
Dongmin Gang ◽  
Kiril Hristov ◽  
Valentin Reys
Keyword(s):  
Black Holes ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Infinite Class ◽  
Gauge Groups ◽  
Higher Derivative ◽  
Hyperbolic Three Manifolds ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$ ℛ . Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-N expansion of supersymmetric partition functions for an infinite class of three-dimensional $$ \mathcal{N} $$ N = 2 SCFTs of class $$ \mathrm{\mathcal{R}} $$ ℛ . We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.

scholarly journals Topological pseudo entropy

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Tatsuma Nishioka ◽  
Tadashi Takayanagi ◽  
Yusuke Taki
Keyword(s):  
Entanglement Entropy ◽  
Three Dimensional ◽  
Partition Functions ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Conformal Field ◽  
Boundary States ◽  
Dimensional Boundary ◽  
Topological Entanglement Entropy ◽  
Chern Simons

Abstract We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop insertions. Partition functions with knotted Wilson loops are directly related to topological pseudo (Rényi) entropies. We also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional conformal field theories (CFTs), and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, we define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states. As a byproduct, we find that the topological interface entropy for rational CFTs has a contribution identical to the topological entanglement entropy on a torus.

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