Non-semisimple Gauge Group Research Articles

A topological field theory for Milnor's triple linking number

The subject of this work is a topological field theory with a non-semisimple gauge group and local observables that are both metric independent and gauge invariant. The observables consist of the holonomies of connections around three arbitrary loops and contain not only three-dimensional vector fields, but also a set of one-dimensional scalar fields. The gauge invariance is achieved by requiring non-trivial gauge transformations in the scalar field sector. The importance of theories of this kind in the statistical physics of linked polymer rings is discussed. The presence of fields of different dimensions is the novel feature of the proposed model, which retains many properties of the non-abelian Chern–Simons field theories and has the advantage to be exactly solvable. Its only one relevant amplitude has been computed here in closed form. From its expression it is possible to isolate the Milnor's triple linking number , a link invariant which has physical applications in the dynamics of fluids and solar magnetohydrodynamics.

Consistent Kaluza-Klein truncations via exceptional field theory

We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO(p,q) and CSO(p,q,r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides $H^{p,q}$, thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D=11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS$_5\times S^5$), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.

New N = 5, 6, 3D gauged supergravities and holography

We study $N=5$ gauged supergravity in three dimensions with compact, non-compact and non-semisimple gauge groups. The theory under consideration is of Chern-Simons type with $USp(4,k)/USp(4)\times USp(k)$ scalar manifold. We classify possible semisimple gauge groups of the $k=2,4$ cases and identify some of their critical points. A number of supersymmetric $AdS_3$ critical points are found, and holographic RG flows interpolating between these critical points are also investigated. As one of our main results, we consider a non-semisimple gauge group $SO(5)\ltimes \mathbf{T}^{10}$ for the theory with $USp(4,4)/USp(4)\times USp(4)$ scalar manifold. The resulting theory describes $N=5$ gauged supergravity in four dimensions reduced on $S^1/\mathbb{Z}_2$ and admits a maximally supersymmetric $AdS_3$ critical point with $Osp(5|2,\mathbb{R})\times Sp(2,\mathbb{R})$ superconformal symmetry. We end the paper with the construction of $SO(6)\ltimes \mathbf{T}^{15}$ gauged supergravity with $N=6$ supersymmetry. The theory admits a half-supersymmetric domain wall as a vacuum solution and may be obtained from an $S^1/\mathbb{Z}_2$ reduction of $N=6$ gauged supergravity in four dimensions.

$ \frac{1}{2} $ -BPS Domain wall from N = 10 three dimensional gauged supergravity

We explicitly construct N = 10 Chern-Simons gaged supergravity in three dimensions with non-semisimple gauge group SO(5) ⋉ T 10. The gauge group is embedded in E 6(−14) which is the isometry group of the 32-dimensional scalar manifold E 6(−14)/SO(10) × U(1). The resulting theory is on-shell equivalent to SO(5) Yang-Mills gauged supergravity coming from dimensional reduction on S 1 of SO(5) N = 5 gauged supergravity in four dimensions. We discuss the spectrum of the corresponding reduction. The SO(5) ⋉ T 10 gauged supergravity, describing the reduced theory, admits a $ \frac{1}{2} $ -BPS domain wall vacuum solution whose explicit form is also given. This provides an example of a domain wall in non-maximal gauged supergravity.

Domain walls in three dimensional gauged supergravity

We explicitly construct two Chern-Simons gauged supergravities in three dimensions with N=4 and N=8 supersymmetries and non-semisimple gauge groups. The N=4 theory has scalar manifold $SO(4,3)/SO(4)\times SO(3)$ with the gauge group $SO(3)\ltimes (\mathbf{T}^3,\hat{\mathbf{T}}^3)$. The theory describes (1,0) six dimensional supergravity reduced on an SU(2) group manifold. The equivalent Yang-Mills type gauged supergravity has SO(3) gauge group coupled to three massive vector fields. The N=8 theory is described by $SO(8,8)/SO(8)\times SO(8)$ scalar manifold, and the gauge group is given by $SO(8)\ltimes \mathbf{T}^{28}$. The theory is a truncation of the $SO(8)\ltimes \mathbf{T}^{28}$ gauged N=16 theory with scalar manifold $E_{8(8)}/SO(16)$ and can be obtained by an S^7 compactification of type I theory in ten dimensions. Domain wall solutions of both gauged supergravities are analytically found and can be uplifted to higher dimensions. These provide domain wall vacua in the three dimensional gauged supergravity framework which might be useful for the study of Domain Wall$_3$/QFT$_2$ correspondence.

Exceptional flux compactifications

AbstractWe consider type II (non-)geometric flux backgrounds in the absence of brane sources, and construct their explicit embedding into maximal gaugedD= 4 supergravity. This enables one to investigate the critical points, mass spectra and gauge groups of such backgrounds. We focus on a class of type IIA geometric vacua and find a novel, nonsupersymmetric and stable AdS vacuum in maximal supergravity with a non-semisimple gauge group. Our construction relies on a non-trivial mapping between SL(2) × SO(6,6) fluxes, SU(8) mass spectra and gaugings of E7(7)subgroups.

Noncommutative [formula omitted] theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θμν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.

Non-Semisimple and Complex Gaugings of N=16 Supergravity

Maximal and non-maximal supergravities in three dimensions allow for a large variety of semisimple (Chern-Simons) gauge groups. In this paper, we analyze non-semisimple and complex gauge groups that satisfy the pertinent consistency relations for a maximal (N=16) gauged supergravity to exist. We give a general procedure how to generate non-semisimple gauge groups from known admissible semisimple gauge groups by a singular boost within E_{8(8)}. Examples include the theories with gauge group SO(8) x T_{28} that describe the reduction of IIA/IIB supergravity on the seven-sphere. In addition, we exhibit two `strange embeddings' of the complex gauge group SO(8,C) into (real) E_{8(8)} and prove that both can be consistently gauged. We discuss the structure of the associated scalar potentials as well as their relation to those of D>3 gauged supergravities.

Chern–Simons vs. Yang–Mills gaugings in three dimensions

Recently, gauged supergravities in three dimensions with Yang–Mills and Chern–Simons type interactions have been constructed. In this article, we demonstrate that any gauging of Yang–Mills type with semisimple gauge group G 0, possibly including extra couplings to massive Chern–Simons vectors, is equivalent on-shell to a pure Chern–Simons type gauging with non-semisimple gauge group G 0⋉ T⊂ G , where T is a certain translation group, and where G is the maximal global symmetry group of the ungauged theory. We discuss several examples.

Chern–Simons field theories with non-semisimple gauge group of symmetry

The subject of this work is a class of Chern–Simons field theories with non-semisimple gauge group, which may well be considered as the most straightforward generalization of an Abelian Chern–Simons field theory. As a matter of fact, these theories, which are characterized by a non-semisimple group of gauge symmetry, have cubic interactions like those of non-Abelian Chern–Simons field theories, but are free from radiative corrections. Moreover, at the tree level in the perturbative expansion, there are only two connected tree diagrams, corresponding to the propagator and to the three vertex originating from the cubic interaction terms. For such theories it is derived here a set of BRST invariant observables, which lead to metric independent amplitudes. The vacuum expectation values of these observables can be computed exactly. From their expressions it is possible to isolate the Gauss linking number and an invariant of the Milnor type, which describes the topological relations among three or more closed curves.

New topological terms in gauge invariant actions

Abstract For gauge theories of nonsemisimple gauge groups, we construct a new class of gauge invariant terms in even space-time dimensions involving nontrivial Lie algebra cohomology classes.

Anomaly cancellations and compactifications in the SO(32) superstring theory.

Some aspects of anomaly cancellations and possible compactifications in the SO(32) superstring theory are discussed. A low-energy nonsemisimple gauge group often results from compactification. It requires that the massive modes of Kaluza-Klein space contribute to the gauge and mixed anomalies in four dimensions to implement the cancellations achieved in ten dimensions. Possible obstructions to compactifications due to surface terms are pointed out.

Color Confinement in Quantum Chromodynamics. II

has been imposed on physical states Iphys) on the assumption of the absence of the spontaneous symmetry breaking with respect to the color charge Qa. **) Since the condition (1·2) puts only a constraint on the total color charge of the state Iphys) integrated over the whole three-dimensional space, this condition may not seem to be sufficient for preventing the colored objects from being observed locally. This objection applies to the cases of the charges constituting a symmetry group which is not semisimpleor which allows the existence of local observables behaving nontrivially under it. For instance, in QED having a non-semisimple gauge group U(1), the observation of electrically charged objects is certainly possible in the chargeless state composed of an electron on the earth and a positron behind the moon. In the case of the rotation group SU(2), it is a (semi)simple group, but rotation-group~variant local observables such as angular-momentum density allow us to measure the spin of a particle in the decay products of a spinless particle. Contrary to these cases, the semisimplicity of the color SU(3) and the absence of colored local observables in QCD have been shown in Ref. 1) to protect the colored particles from being observed in the colorless total state satisfying (1' 2). Let Q 1 and Q 2 be spacetime regions spacelikely separated, the former of which is in our side and the