Real SU Research Articles

W boson mass and grand unification via the type-II seesaw-like mechanism

We propose an SU(5) GUT model extended with two additional pairs of 10 representation vector-like fermions. The CDF collaboration W boson mass anomaly is explained by using the VEV of a real SU(2)L triplet scalar coming from the 24 representation Higgs. The vector-like fermions are decomposed partly into vector-like quark doublets. Those vector-like quark doublets acquire mass from two sources; through the Yukawa interaction with the real SU(2)L triplet via a type-II seesaw-like mechanism. And, they acquire mass from the 24 representation Higgs. We assume that the mass for the vector-like quark doublets is expressed in terms of the real triplets mass. By combining the constraints on the vector-like quark masses with those on the heavy Higgs boson masses, we can obtain the narrow allowed mass ranges for the vector-like quark doublet and the real triplet. Therefore, our model can be tested in searches for these particles in the near future. In addition, the two additional pairs of vector-like fermions allow the SM gauge couplings to unify successfully at MGUT≈5.1×1015 GeV. Our model is also testable by the future Hyper-Kamiokande experiment via the proton decay lifetime τp(p→π0e+)<1.0×1035 years.

Closing the window on WIMP Dark Matter

We study scenarios where Dark Matter is a weakly interacting particle (WIMP) embedded in an ElectroWeak multiplet. In particular, we consider real SU(2) representations with zero hypercharge, that automatically avoid direct detection constraints from tree-level Z-exchange. We compute for the first time all the calculable thermal masses for scalar and fermionic WIMPs, including Sommerfeld enhancement and bound states formation at leading order in gauge boson exchange and emission. WIMP masses of few hundred TeV are shown to be compatible both with s-wave unitarity of the annihilation cross-section, and perturbativity. We also provide theory uncertainties on the masses for all multiplets, which are shown to be significant for large SU(2) multiplets. We then outline a strategy to probe these scenarios at future experiments. Electroweak 3-plets and 5-plets have masses up to about 16 TeV and can efficiently be probed at a high energy muon collider. We study various experimental signatures, such as single and double gauge boson emission with missing energy, and disappearing tracks, and determine the collider energy and luminosity required to probe the thermal Dark Matter masses. Larger multiplets are out of reach of any realistic future collider, but can be tested in future gamma -ray telescopes and possibly in large-exposure liquid Xenon experiments.

Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity

The successful background-independent quantization of Loop Quantum Gravity relies on the key observation that classical General Relativity can be cast into the connection-dynamical formalism with the structure group of SU(2). Due to this particular formalism, Loop Quantum Gravity was generally considered as a quantization scheme that applies only to General Relativity. However, we will show that the nonperturbative quantization procedure of Loop Quantum Gravity can be extended to a rather general class of metric theories of gravity, which have received increased attention recently due to motivations coming form cosmology and astrophysics. In particular, we will first introduce how to reformulate the 4-dimensional metric f(R) theories of gravity, as well as Brans-Dicke theory, into connection-dynamical formalism with real SU(2) connections as configuration variables. Through these formalisms, we then outline the nonpertubative canonical quantization of the f(R) theories and Brans-Dicke theory by extending the loop quantization scheme of General Relativity.

Loop Quantum Brans-Dicke Theory

The loop quantization of Brans-Dicke theory (with coupling parameter ) is studied. In the geometry-dynamical formalism, the canonical structure and constraint algebra of this theory are similar to those of general relativity coupled with a scalar field. The connection dynamical formalism of the Brans-Dicke theory with real su(2)-connections as configuration variables is obtained by canonical transformations. The quantum kinematical Hilbert space of Brans-Dicke theory is constituted as that of loop quantum gravity coupled with a polymer-like scalar field. The Hamiltonian constraint is promoted as a well defined operator to represent quantum dynamics. This formalism enable us to extend the scheme of non-perturbative loop quantum gravity to the Brans-Dicke theory.

SU(2) gauge theory of gravity with topological invariants

The most general gravity Lagrangian in four dimensions contains three topological densities, namely Nieh-Yan, Pontryagin and Euler, in addition to the Hilbert-Palatini term. We set up a Hamiltonian formulation based on this Lagrangian. The resulting canonical theory depends on three parameters which are coefficients of these terms and is shown to admit a real SU(2) gauge theoretic interpretation with a set of seven first-class constraints. Thus, in addition to the Newton's constant, the theory of gravity contains three (topological) coupling constants, which might have non-trivial imports in the quantum theory, e.g. in quantum geometry.

Topological parameters in gravity

We present the Hamiltonian analysis of the theory of gravity based on a Lagrangian density containing Hilbert-Palatini term along with three topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these topological terms modifies the symplectic structure non-trivially. The resulting canonical theory develops a dependence on three parameters which are coefficients of these terms. In the time gauge, we obtain a real SU (2) gauge theoretic description with a set of seven first class constraints corresponding to three SU (2) rotations, three spatial diffeomorphism and one to evolution in a timelike direction. Inverse of the coefficient of Nieh-Yan term, identified as Barbero-Immirzi parameter, acts as the coupling constant of the gauge theory.

Charging the superconformal index

The superconformal index is an important invariant of superconformal field theories. In this note we refine the superconformal index by inserting the charge conjugation operator C. We construct a matrix integral for this charged index for N=4 SYM with SU(N) gauge group. The key ingredient for the construction is a "charged character," which reduces to Tr(C) for singlet representations of the gauge group. For each irreducible real SU(N) representation, we conjecture that this charged character is equal to the standard character for a corresponding representation of SO(N+1) or SP(N-1), for N even or odd respectively. The matrix integral for the charged index passes tests for small N and for N -> infinity. Like the ordinary superconformal index, for N=4 SYM the charged index is independent of N in the large-N limit.

Topological interpretation of Barbero-Immirzi parameter

We set up a canonical Hamiltonian formulation for a theory of gravity based on a Lagrangian density made up of the Hilbert-Palatini term and, instead of the Holst term, the Nieh-Yan topological density. The resulting set of constraints in the time gauge are shown to lead to a theory in terms of a real SU(2) connection which is exactly the same as that of Barbero and Immirzi with the coefficient of the Nieh-Yan term identified as the inverse of the Barbero-Immirzi parameter. This provides a topological interpretation for this parameter. Matter coupling can then be introduced in the usual manner, without changing the universal topological Nieh-Yan term.

Lorentz-invariant solutions of the classical Yang-Mills equations

A ‘gauge’ representation of the noncompact group SL(2,C) is defined. All the corresponding invariant (singular) solutions of the classical Yang-Mills equations in Minkowski space are found. It is shown that they are related to a family of real SU(2) x SU(2)-invariant Euclidean solutions containing the self-dual (one-instanton) configurations.

The Baker–Campbell–Haussdorff formula for the SU(2) supergroups

In the theory of supersymmetric SU(2) Yang–Mills fields described on the 8th dimensional superspace, the local gauge transformations constitute a group whose Lie algebra has its coefficients in the Weyl-spinorial-Grassmann algebra. The coefficients can be taken to be chiral elements, real or complex. This last case is the most general one and contains all others of interest for developing physical models. We present here a Baker–Campbell–Haussdorff formula for the complex SU(2) supergroup. The formula gives the finite form for each element of the supergroup in terms of the local fields entering into the infinitesimal (complex) superscalar generator. Thereafter we exhibit, as a particular case, a BCH-expression for the real SU(2) supergroup which completes previous results already reported for the chiral SU(2) supergroups. Moreover, it is shown that, despite the appearance of apparently nonperiodic polynomial terms, the global variety of the real SU(2) supergroup is contained in a variety having the same compact bosonic width as the usual SU(2) pure bosonic variety.

The construction of self-dual solutions to SU(2) gauge theory

Ignoring the problem of sources and singularities, explicit expressions are constructed for the ansatze of Atiyah and Ward. These take an especially simple form in theR gauge of Yang. Some non-linear transformation properties of the self-duality equations in this gauge provide an inductive proof of the ansatze. There is a six-parameter family of these Backlund transformations. They take real SU(2) gauge fields into real SU(1, 1) gauge fields and vice versa.