A new and gauge-invariant littlest Higgs model with T-parity

We inspect the Littlest Higgs model with T-parity, based on a global symmetry SU(5) spontaneously broken to SO(5), in order to elucidate the pathologies it presents due to the non-trivial interplay between the gauge invariance associated to the heavy modes and the discrete T-parity symmetry. In particular, the usual Yukawa Lagrangian responsible for providing masses to the heavy ‘mirror’ fermions is not gauge invariant. This is because it contains an SO(5) quintuplet of right-handed fermions that transforms nonlinearly under SU(5), hence involving in general all SO(5) generators when a gauge transformation is performed and not only those associated to its gauge subgroup. Part of the solution to this problem consists of completing the right-handed fermion quintuplet with T-odd ‘mirror partners’ and a gauge singlet, what has been previously suggested for other purposes. Furthermore, we find that the singlet must be T-even, the global symmetry group must be enlarged, an additional nonlinear sigma field should be introduced to parametrize the spontaneous symmetry breaking and new extra fermionic degrees of freedom are required to give a mass to all fermions in an economic way while preserving gauge invariance. Finally, we derive the Coleman–Weinberg potential for the Goldstone fields using the background field method.

Rank $Q$ E-string on spheres with flux

We consider compactifications of rank \boldsymbol{Q}𝐐 E-string theory on a genus zero surface with no punctures but with flux for various subgroups of the \boldsymbol{\mathrm{E}_8\times \mathrm{SU}(2)}E8×SU(2) global symmetry group of the six dimensional theory. We first construct a simple Wess–Zumino model in four dimensions corresponding to the compactification on a sphere with one puncture and a particular value of flux, the cap model. Using this theory and theories corresponding to two punctured spheres with flux, one can obtain a large number of models corresponding to spheres with a variety of fluxes. These models exhibit interesting IR enhancements of global symmetry as well as duality properties. As an example we will show that constructing sphere models associated to specific fluxes related by an action of the Weyl group of \boldsymbol{\mathrm{E}_8}E8 leads to the S-confinement duality of the \boldsymbol{\mathrm{USp}(2Q)}USp(2𝐐) gauge theory with six fundamentals and a traceless antisymmetric field. Finally, we show that the theories we discuss possess an \boldsymbol{\mathrm{SU}(2)_{\text{ISO}}}SU(2)ISO symmetry in four dimensions that can be naturally identified with the isometry of the two-sphere. We give evidence in favor of this identification by computing the `t Hooft anomalies of the \boldsymbol{\mathrm{SU}(2)_{\text{ISO}}}SU(2)ISO in 4d and comparing them with the predicted anomalies from 6d.

Confinement in 4D: An Attempt at Classical Understanding

In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. We set out to ensure the presence of the massless photons—Goldstone bosons in Abelian theory and their disappearance in the Non-Abelian case—accompanied by the formation of confining strings between charged states. Our formulation avoids using vector fields and instead operates with the basic degrees of freedom that are the scalar fields of a nonlinear σ-model. The Mark 1 model we study turns out to have a large global symmetry group-the 2D diffeomorphism invariance in the Abelian limit, which is isomorphic to the group of all canonical transformations in the classical two dimensional phase space. This symmetry is not present in QED, and we eliminate it by “gauging” this infinite dimensional global group. Introducing additional modifications to the model (Mark 2), we are able to prove that the “Abelian” version is equivalent to the theory of a free photon. Achieving the desired property in the “Non-Abelian” regime turns out to be tricky. We are able to introduce a perturbation that leads to the formation of confining strings in our Mark 1 model. These strings have somewhat unusual properties, in that their profile does not decay exponentially away from the center of the string. In addition, the perturbation explicitly breaks the diffeomorphism invariance. Preserving this invariance in the gauged model as well as achieving confining strings in Mark 2 model remains an open question.

Multi-fixed point numerical conformal bootstrap: a case study with structured global symmetry

In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown non-trivial conformal field theories (CFTs). Here we investigate the extent to which this is possible in the case where the global symmetry group has a product structure. We do this by testing for signatures of fixed points using a mixed-correlator bootstrap calculation with a minimal set of input assumptions. This ‘semi-blind’ approach contrasts with other approaches for probing more complicated groups, which ‘target’ known theories with additional spectral assumptions or use the saturation of the single-correlator bootstrap bound as a starting point. As a case study, we select the space of CFTs with product-group symmetry O(15) ⊗ O(3) in d = 3 dimensions. On the assumption that there is only one relevant scalar (ℓ = 0) singlet operator in the theory, we find a single ‘allowed’ region in our chosen space of scaling dimensions. The scaling dimensions corresponding to two known large-N critical theories, the Heisenberg and the chiral ones, lie on or very near the boundary of this region. The large-N antichiral point lies well outside the ‘allowed’ region, which is consistent with the expectation that the antichiral theory is unstable, and thus has an additional relevant scalar singlet operator. We also find a sharp kink in the boundary of the ‘allowed’ region at values of the scaling dimensions that do not correspond to the (N, M ) = (3, 15) instance of any large-N -predicted O(N ) ⊗ O(M ) critical theory.

The axion quality problem: global symmetry breaking and wormholes

Continuous global symmetries are expected to be broken by gravity, which can lead to important phenomenological consequences. A prime example is the threat that this poses to the viability of the Peccei-Quinn solution to the strong CP problem. In this paper, we explore the impact of wormholes as a source of global symmetry breaking by gravity. We review the current status of wormholes and global symmetries and note that, surprisingly, the axion has a quality problem within non-perturbative Einstein gravity. Although these wormholes lead to a large breaking of global symmetries, we show that their effect is nonetheless relevant for the model building of gauge protected axions. We also find wormhole solutions within two scenarios: (i) an extended global symmetry group within Einstein gravity, and (ii) U(1) wormholes within the low-energy limit of an open String Theory. The former allows us to show that the concept of a global symmetry in General Relativity is somewhat ill-defined. The latter illustrates that for motivated values of the string coupling constant, axions appear to have a quality problem within the open String Theory we consider.

Pseudoscalar glueballs in the Klebanov-Strassler theory

In this paper we describe a pseudoscalar subsector of the Klebanov-Strassler model. This subsector completes the holographic reconstruction of the spectrum of the lowest-lying glueball states, which are singlet under the global symmetry group SU(2) × SU(2). We derive the linearized supergravity equations for the pseudoscalar fluctuations and analyze their spectrum. The system of equations is shown to be compatible with six eigenmodes, as expected from supersymmetry. Our numerical analysis allows to reliably extract four of the corresponding towers. Their values match well the eigenvalues of the 0++ scalar states known from an earlier work. Assuming the masses of 0++ as a reference, we compare the lightest states of the holographic spectrum with lattice calculations in the quenched QCD at Nc = 3 and Nc = ∞.

Models of hypercolor based on symplectic gauge group with three heavy vectorlike hyperquarks

We study possibilities to extend the Standard Model (SM) by three flavors of vectorlike heavy quarks in pseudoreal representation of symplectic hypercolor gauge group. This extension of SM predicts a rich spectra of heavy composite hypermesons and hyperbaryons (all of them carry integer spins) including 14 pseudo-Nambu–Goldstone states emerging in dynamical breaking of the global symmetry group of the H-quarks, [Formula: see text], to its Sp(6) subgroup. The properties of the lightest states depend strongly on the choice of heavy-quark hypercharges. Our focus is placed on the variants of the model with partially composite Higgs boson, i.e. the experimentally observed boson comprised the elementary SM Higgs and a mixture of H-hadrons.

Local and global color symmetries of a symmetrical pattern

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.

The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors

We propose a cohomological modelling schema of quantum state spaces and their connectivity structures in relation to the formulation of global geometric phase phenomena. In the course of this schema, we introduce the notion of Hermitian differential line sheaves or unitary rays and classify their gauge equivalence classes in terms of a global differential invariant given by the de Rham cohomology class of the curvature. Furthermore, we formulate and interpret physically the curvature recognition integrality theorem for unitary rays. Using this recognition theorem, we define the notion of a quantum spectral beam and show that it has an affine space structure with structure group given by the characters of the fundamental group.

A SCHEME FOR COMPLEMENTARITY AND HIGGS PHASE ANALYSES

We introduce a simple dynamical scheme to supplement the complementarity and Higgs phase analyses of composite models with semi-simple metacolor groups. The critical couplings which signal the dynamical breakdown of the various simple groups contained in the metacolor semi-simple group determine the order of appearance of the condensates of the simple groups. Together with the Higgs phase analysis, it helps to determine the global symmetry of the fermion composite. The global symmetry group will eventually be gauged to form the low energy dynamical symmetry group of the composite.