GAUGE GROUP AND PHASES OF SUPERFLUID 3He

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

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Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

Journal of High Energy Physics ◽

10.1007/jhep12(2020)189 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Fridrich Valach ◽

Donald R. Youmans

Keyword(s):

Quantum Mechanics ◽

Partition Function ◽

Gauge Group ◽

Path Integral ◽

Coadjoint Orbits ◽

Two Dimensional ◽

Edge States ◽

Class Constraint ◽

Action Functional ◽

Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

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Vector dark matter from split SU(2) gauge bosons

Journal of High Energy Physics ◽

10.1007/jhep07(2021)089 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Zexi Hu ◽

Chengfeng Cai ◽

Yi-Lei Tang ◽

Zhao-Huan Yu ◽

Hong-Hao Zhang

Keyword(s):

Dark Matter ◽

Gauge Group ◽

Measurement Data ◽

Indirect Detection ◽

Gauge Bosons ◽

Dark Matter Relic Density ◽

Matter Model ◽

Direct And Indirect Detection ◽

Numerous Parameter ◽

Dark Matter Model

Abstract We propose a vector dark matter model with an exotic dark SU(2) gauge group. Two Higgs triplets are introduced to spontaneously break the symmetry. All of the dark gauge bosons become massive, and the lightest one is a viable vector DM candidate. Its stability is guaranteed by a remaining Z2 symmetry. We study the parameter space constrained by the Higgs measurement data, the dark matter relic density, and direct and indirect detection experiments. We find numerous parameter points satisfying all the constraints, and they could be further tested in future experiments. Similar methodology can be used to construct vector dark matter models from an arbitrary SO(N) gauge group.

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A composite Higgs with a heavy composite axion

Journal of High Energy Physics ◽

10.1007/jhep12(2020)094 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Tony Gherghetta ◽

Minh D. Nguyen

Keyword(s):

Cp Violation ◽

Gauge Group ◽

Scalar Fields ◽

Higgs Model ◽

Global Symmetry ◽

Color Group ◽

High Scale ◽

Axion Mass ◽

Composite Higgs ◽

The Standard Model

Abstract We consider the strong dynamics associated with a composite Higgs model that simultaneously produces dynamical axions and solves the strong CP problem. The strong dynamics arises from a new Sp or SU(4) hypercolor gauge group containing QCD colored hyperfermions that confines at a high scale. The hypercolor global symmetry is weakly gauged by the Standard Model electroweak gauge group and an enlarged color group, SU(N + 3) × SU(N)′. When hyperfermion condensates form, they not only lead to an SU(5)/SO(5) composite Higgs model but also spontaneously break the enlarged color group to SU(3)c× SU(N)D. At lower energies, the SU(N)D group confines, producing two dynamical axions that eliminates all CP violation. Furthermore, small instantons from the SU(N)′ group can enhance the axion mass, giving rise to TeV scale axion masses that can be detected at collider experiments. Our model provides a way to unify the composite Higgs with dynamical axions, without introducing new elementary scalar fields, while also extending the range of axion masses that addresses the strong CP problem.

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Mocking the u-plane integral

Research in the Mathematical Sciences ◽

10.1007/s40687-021-00280-5 ◽

2021 ◽

Vol 8 (3) ◽

Author(s):

Georgios Korpas ◽

Jan Manschot ◽

Gregory W. Moore ◽

Iurii Nidaiev

Keyword(s):

Asymptotic Behavior ◽

Gauge Theory ◽

Entire Function ◽

Gauge Group ◽

Strong Coupling ◽

Modular Forms ◽

Correlation Functions ◽

Coulomb Branch ◽

Mock Modular Forms ◽

Donaldson Invariants

AbstractThe u-plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

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