scholarly journals The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Benjamin Assel ◽  
Stefano Cremonesi
Keyword(s):  
Fixed Points ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Singular Locus ◽  
Low Energy ◽  
Global Symmetry ◽  
Local Geometry ◽  
Coulomb Branch ◽  
Energy Theory ◽  
Mirror Theory

We derive the algebraic description of the Coulomb branch of 3d \mathcal{N}=4𝒩=4USp(2N)USp(2N) SQCD theories with N_fNf fundamental hypermultiplets and determine their low energy physics in any vacuum from the local geometry of the moduli space, identifying the interacting SCFTs which arise at singularities and possible extra free sectors. The SCFT with the largest moduli space arises at the most singular locus on the Coulomb branch. For N_f > 2NNf>2N (good theories) it sits at the origin of the conical variety as expected. For N_f =2NNf=2N we find two separate most singular points, from which the two isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs sitting at any of these two vacua have only odd dimensional Coulomb branch generators, which transform under an accidental SU(2)SU(2) global symmetry. We provide a direct derivation of their moduli spaces of vacua, and propose a Lagrangian mirror theory for these fixed points. For 2 \leq N_f < 2N2≤Nf<2N the most singular locus has one or two extended components, for N_fNf odd or even, and the low energy theory involves an interacting SCFT of one of the above types, plus free twisted hypermultiplets. For N_f=0,1Nf=0,1 the Coulomb branch is smooth. We complete our analysis by studying the low energy theory at the symmetric vacuum of theories with N < N_f \le 2NN<Nf≤2N, which exhibits a local Seiberg-like duality.

scholarly journals The Infrared Physics of Bad Theories

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Benjamin Assel ◽  
Stefano Cremonesi
Keyword(s):  
Global Symmetries ◽  
Fixed Points ◽  
Moduli Space ◽  
Low Energy ◽  
Partition Functions ◽  
Local Geometry ◽  
Coulomb Branch ◽  
Algebraic Description ◽  
Symmetric Vacuum ◽  
Energy Physics

We study the complete moduli space of vacua of 3d \mathcal{N}=4𝒩=4U(N)U(N) SQCD theories with N_fNf fundamentals, building on the algebraic description of the Coulomb branch, and deduce the low energy physics in any vacuum from the local geometry of the moduli space. We confirm previous claims for good and ugly SQCD theories, and show that bad theories flow to the same interacting fixed points as good theories with additional free twisted hypermultiplets. A Seiberg-like duality proposed for bad theories with N \le N_f \le 2N-2N≤Nf≤2N−2 is ruled out: the spaces of vacua of the putative dual theories are different. However such bad theories have a distinguished vacuum, which preserves all the global symmetries, whose infrared physics is that of the proposed dual. We finally explain previous results on sphere partition functions and elucidate the relation between the UV and IR RR-symmetry in this symmetric vacuum.

scholarly journals Hasse diagrams for 3d $$ \mathcal{N} $$ = 4 quiver gauge theories — Inversion and the full moduli space

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Julius F. Grimminger ◽  
Amihay Hanany
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Gauge Theories ◽  
Hasse Diagram ◽  
Coulomb Branch ◽  
Hasse Diagrams

Abstract We study Hasse diagrams of moduli spaces of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories. The goal of this work is twofold: 1) We introduce the notion of inverting a Hasse diagram and conjecture that the Coulomb branch and Higgs branch Hasse diagrams of certain theories are related through this operation. 2) We introduce a Hasse diagram to map out the entire moduli space of the theory, including the Coulomb, Higgs and mixed branches. For theories whose Higgs and Coulomb branch Hasse diagrams are related by inversion it is straight forward to generate the Hasse diagram of the entire moduli space. We apply inversion of the Higgs branch Hasse diagram in order to obtain the Coulomb branch Hasse diagram for bad theories and obtain results consistent with the literature. For theories whose Higgs and Coulomb branch Hasse diagrams are not related by inversion it is nevertheless possible to produce the Hasse diagram of the full moduli space using different methods. We give examples for Hasse diagrams of the entire moduli space of theories with enhanced Coulomb branches.

scholarly journals Higgs Branch, Hyper-Kähler Quotient and Duality in SUSY N = 2 Yang–Mills Theories

1997 ◽  
Vol 12 (27) ◽  
pp. 4907-4931 ◽  
Author(s):  
I. Antoniadis ◽  
B. Pioline
Keyword(s):  
Moduli Space ◽  
Gauge Theories ◽  
Geometric Interpretation ◽  
Low Energy ◽  
Target Space ◽  
Field Theories ◽  
Yang Mills ◽  
Coulomb Phase ◽  
Supersymmetric Field Theories ◽  
Energy Theory

Low-energy limits of N = 2 supersymmetric field theories in the Higgs branch are described in terms of a nonlinear four-dimensional σ-model on a hyper-Kähler target space, classically obtained as a hyper-Kähler quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low-energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg–Witten SU(2) theory with Nf flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on ℝ4. By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a U(1) N = 2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg–Witten's theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of U(Nc)Nf flavors and U(Nf-Nc)Nf flavors theories, by using a geometric interpretation due to Biquard et al. This duality may be relevant for understanding Seiberg's conjectured duality Nc ↔ Nf-Nc in N = 1 SUSY SU(Nc) gauge theories.

scholarly journals 3d mirrors of the circle reduction of twisted A2N theories of class S

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Emanuele Beratto ◽  
Simone Giacomelli ◽  
Noppadol Mekareeya ◽  
Matteo Sacchi
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Strong Support ◽  
Three Dimensions ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Group Flow ◽  
Mirror Theory

Abstract Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted A2N theories of class S in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.

scholarly journals Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

2020 ◽  
Vol 9 (6) ◽  
Author(s):  
Philip Argyres ◽  
Antoine Bourget ◽  
Mario Martone
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Large Majority ◽  
Field Theories ◽  
Coordinate Ring ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Complex Dimension ◽  
Rank 2

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional \mathcal{N}\geq 3𝒩≥3 superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an \mathcal{N}=2𝒩=2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic \mathcal{N}=3𝒩=3 theories.

scholarly journals MODULI SPACE OF GLOBAL SYMMETRY IN N=1 SUPERSYMMETRIC THEORIES AND THE QUASI-NAMBU–GOLDSTONE BOSONS

1999 ◽  
Vol 14 (15) ◽  
pp. 2397-2430 ◽  
Author(s):  
MUNETO NITTA
Keyword(s):  
Moduli Space ◽  
Arbitrary Function ◽  
Singular Points ◽  
Low Energy ◽  
Global Symmetry ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Generic Points ◽  
Supersymmetric Theories

We derive the moduli space of the global symmetry in N=1 supersymmetric theories. We show that, at the generic points, it coincides with the space of quasi-Nambu–Goldstone (QNG) bosons, which appear besides the ordinary Nambu–Goldstone (NG) bosons when the global symmetry G breaks down spontaneously to its subgroup H with preservation of N=1 supersymmetry. At the singular points, most of the NG bosons change to QNG bosons and the unbroken global symmetry is enhanced. The G orbits parametrized by the NG bosons are the fiber at the moduli space and the singular points correspond to the point where the H orbit (in the G orbit) shrinks. We also show that the low energy effective Lagrangian is the arbitrary function of the moduli parameters.

scholarly journals JACOBI COHOMOLOGY, LOCAL GEOMETRY OF MODULI SPACES, AND HITCHIN CONNECTIONS

2006 ◽  
Vol 92 (3) ◽  
pp. 545-580 ◽  
Author(s):  
ZIV RAN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Fields ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Local Geometry ◽  
Parameter Spaces ◽  
Natural Action ◽  
Lie Bracket ◽  
Moduli Spaces Of Curves

We develop some cohomological tools for the study of the local geometry of moduli and parameter spaces in complex Algebraic Geometry. Notably, we develop canonical formulae for the differential operators of arbitrary order and their natural action on suitable `natural' modules (for example, functions); in particular, we obtain a formula, in terms of the moduli problem, for the Lie bracket of vector fields on a moduli space. As an application, we obtain another construction and proof of flatness for the familiar KZW or Hitchin connection on moduli spaces of curves.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anthony Ashmore ◽  
Sebastian Dumitru ◽  
Burt A. Ovrut
Keyword(s):  
Line Bundle ◽  
Supersymmetry Breaking ◽  
Moduli Space ◽  
Initial Conditions ◽  
Low Energy ◽  
Strongly Coupled ◽  
Hidden Sector ◽  
Effective Lagrangian ◽  
Soft Supersymmetry Breaking ◽  
M Theory

Abstract The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

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