non-Abelian Sector Research Articles

Gravitational wave background from non-Abelian reheating after axion-like inflation

A pseudoscalar inflaton φ, coupled to the topological charge density FF̃ of a non-Abelian sector, can decay to gauge bosons (φ ⟶ gg), which may thermalize rapidly. The friction felt by φ is then increased by non-Abelian “strong sphalerons”, leading to a self-amplifying process that can efficiently heat up the medium. We determine a lower bound for the gravitational wave production rate from such a process, originating via hydrodynamic fluctuations and particle collisions, in terms of a minimal number of parameters. Only a moderate fraction of energy density is converted to gravitational waves, suggesting that non-Abelian models may avoid the overproduction observed in some Abelian cases.

New BPS solitons in mathcal{N} = 4 gauged supergravity and black holes in Einstein-Yang-Mills-dilaton theory

We start by revisiting the problem of finding BPS solutions in mathcal{N} = 4 SU (2) × SU (2) gauged supergravity. We report on a new supersymmetric solution in the Abelian sector of the theory, which describes a soliton that is regular everywhere. The solution is 1/4 BPS and can be obtained from a double analytic continuation of a planar solution found by Klemm in hep-th/9810090. Also in the Abelian sector, but now for a spherically symmetric ansatz we find a new solution whose supersymmetric nature was overlooked in the previous literature. Then, we move to the non-Abelian sector of the theory by considering the meron ansatz for SU (2). We construct electric-meronic and double-meron solutions and show that the latter also leads to 1/4 BPS configurations that are singular and acquire an extra conformal Killing vector. We then move beyond the supergravity embedding of this theory by modifying the self-interaction of the scalar, but still within the same meron ansatz for a single gauge field, which is dilatonically coupled with the scalar. We construct exact black holes for two families of self-interactions that admit topologically Lifshitz black holes, as well as other black holes with interesting causal structures and asymptotic behavior. We analyze some thermal properties of these spacetimes.

Equivalence between vortices, twists, and chiral gauge fields in the Kitaev honeycomb lattice model

We demonstrate that $\mathbb{Z}_2$ gauge transformations and lattice deformations in Kitaev's honeycomb lattice model can have the same description in the continuum limit of the model in terms of chiral gauge fields. The chiral gauge fields are coupled to the Majorana fermions that satisfy the Dirac dispersion relation in the non-Abelian sector of the model. For particular values, the effective chiral gauge field becomes equivalent to the $\mathbb{Z}_2$ gauge field, enabling us to associate effective fluxes to lattice deformations. Motivated by this equivalence, we consider Majorana-bounding $\pi$ vortices and Majorana-bounding lattice twists and demonstrate that they are adiabatically connected to each other. This equivalence opens the possibility for novel encoding of Majorana-bounding defects that might be easier to realise in experiments.

Scheme dependence of asymptotically free solutions

Recent studies have provided evidence for the existence of new asymptotically free trajectories in non-Abelian particle models without asymptotic symmetry in the high-energy limit. We extend these results to a general mathrm {SU}(N_{mathrm {L}})times mathrm {SU}(N_{mathrm {c}}) Higgs-Yukawa model that includes the non-Abelian sector of the standard model, finding further confirmation for such scenarios for a wide class of regularizations that account for threshold behavior persisting to highest energies. We construct these asymptotically free trajectories within conventional overline{text {MS}} schemes and systematic weak coupling expansions. The existence of these solutions is argued to be a scheme-independent phenomenon, as demonstrated for mass-dependent schemes based on general momentum-space infrared regularizations. A change of scheme induces a map of the theory’s coupling space onto itself, which in the present case also translates into a reparametrization of the space of asymptotically free solutions.

Non Abelian T-duality in Gauged Linear Sigma Models

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

Non-Abelian gauge preheating

We study preheating in models where a scalar inflaton is directly coupled to a non-Abelian $SU(2)$ gauge field. In particular, we examine ${m}^{2}{\ensuremath{\phi}}^{2}$ inflation with a conformal, dilatonlike coupling to the non-Abelian sector. We describe a numerical scheme that combines lattice gauge theory with standard finite difference methods applied to the scalar field. We show that a significant tachyonic instability allows for efficient preheating, which is parametrically suppressed by increasing the non-Abelian self-coupling. Additionally, we comment on the technical implementation of the evolution scheme and setting initial conditions.

Single-step de Sitter vacua from nonperturbative effects with matter

A scenario of moduli stabilisation based on the interplay between closed and open string sectors is explored in a bottom-up approach. We study N=1 effective supergravities inspired by type IIB orientifold constructions that include background fluxes and non-perturbative effects. The former generate the standard flux superpotential for the axiodilaton and complex structure moduli. The latter can be induced by gaugino condensation in a non-Abelian sector of D7-branes and involve the overall Kaehler modulus of the compactification as well as matter fields. We analyse the dynamics of this coupled system and show that it is compatible with single-step moduli stabilisation in a metastable de Sitter vacuum. A novelty of the scenario is that the F-term potential suffices to generate a positive cosmological constant and to stabilise all moduli, except for a flat direction that can be either lifted by a mass term or eaten up by an anomalous U(1).

Correlation Lengths and Topological Entanglement Entropies of Unitary and Nonunitary Fractional Quantum Hall Wave Functions

Using the newly developed matrix product state formalism for non-Abelian fractional quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a nonunitary conformal field theory (CFT) can describe the bulk of a gapped FQH phase. We show that the nonunitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of a Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has an infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-Abelian states with and without quasiholes. For the first time in the FQH effect the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the nonunitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the composite fermion Jain state at equal filling.

Many-body study of a quantum point contact in the fractional quantum Hall regime atν=5/2

We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors 1/3 and 5/2. By using exact diagonalizations in the cylinder geometry we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor 5/2 we identify the conformal towers of many-body eigenstates including the non-Abelian sector. By a Monte-Carlo technique we compute the various scaling exponents that characterize the edge modes. In the case of hard-core interactions whose ground states are exact model wavefunction we find equality of neutral and charged velocities for the Pfaffian state both bosonic and fermionic.

On the 1-loop effective action for the IKKT model and non-commutative branes

We study the one-loop effective action of the IKKT or IIB model on a 4-dimensional non-commutative brane background. The trace-U(1) sector is governed by non-commutativity, and leads - assuming no SUSY breaking - to a higher-derivative effective action. In contrast, the non-Abelian sector at low energies reduces to SU(n) N=4 Super-Yang-Mills on the brane, with a global SO(9,1) symmetry broken spontaneously by the background. In the Coulomb branch, we recover the leading contribution to the Dirac-Born-Infeld (DBI) action, exhibiting a S^5 \times AdS^5 bulk geometry around a stack of branes. SUSY may be broken by compact extra dimensions M^4 x K, leading to an induced gravitational action on M^4 due to the trace-U(1) sector. The one-loop effective action is UV finite on such backgrounds, and the UV/IR mixing is non-pathological.

Phenomenology of a three-family standardlike string model

We discuss the phenomenology of a three-family supersymmetric Standard-like Model derived from the orientifold construction, in which the ordinary chiral states are localized at the intersection of branes at angles. In addition to the Standard Model group, there are two additional U(1)' symmetries, one of which has family non-universal and therefore flavor changing couplings, and a quasi-hidden non-abelian sector which becomes strongly coupled above the electroweak scale. The perturbative spectrum contains a fourth family of exotic (SU(2)- singlet) quarks and leptons, in which, however, the left-chiral states have unphysical electric charges. It is argued that these decouple from the low energy spectrum due to hidden sector charge confinement, and that anomaly matching requires the physical left-chiral states to be composites. The model has multiple Higgs doublets and additional exotic states. The moduli-dependent predictions for the gauge couplings are discussed. The strong coupling agrees with experiment for reasonable moduli, but the electroweak couplings are too small.

Spontaneous symmetry breaking and the renormalization of the Chern-Simons term

We calculate the one-loop perturbative correction to the coefficient of the Chern-Simons term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual U(1) symmetry, radiative corrections do not change the coefficient of the Chern-Simons term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant Chern-Simons term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the Chern-Simons term is a discontinuous function over the phase diagram of the theory.

Saddle-point solutions in Yang-Mills-dilaton theory.

The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analitical and numerical methods. In the abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the nonabelian sector there exist a countable family of globally regular solutions which are purely magnetic but have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with increasing number of unstable modes. The existence and instability of these solutions are "explained" by the Morse-theory argument recently proposed by Sudarsky and Wald.