Adjoint Multiplet Research Articles

Unification of elementary forces in gauge SL(2N,C) theories

We argue that the gauge SL(2N,C) theories may point to a possible way where the known elementary forces, including gravity, could be consistently unified. Remarkably, while all related gauge fields are presented in the same adjoint multiplet of the SL(2N,C) symmetry group, the tensor field submultiplet providing gravity can be naturally suppressed in the weak-field approach developed for accompanying tetrad fields. As a result, the whole theory turns out to effectively possess the local SL(2,C)×SU(N) symmetry so as to naturally lead to the SL(2,C) gauge gravity, on the one hand, and the SU(N) grand unified theory, on the other. Since all states involved in the SL(2N,C) theories are additionally classified according to their spin values, many possible SU(N) GUTs – including the conventional one-family SU(5) theory – appear not to be relevant for the standard 1/2 spin quarks and leptons. Meanwhile, the SU(8) grand unification for all three families of composite quarks and leptons that stems from the SL(16,C) theory seems to be of special interest that is studied in some detail.

Split Dirac supersymmetry: An ultraviolet completion of Higgsino dark matter

Motivated by the observation that the Higgs quartic coupling runs to zero at an intermediate scale, we propose a new framework for models of split supersymmetry, in which gauginos acquire intermediate scale Dirac masses of $\sim 10^{8-11}$ GeV. Scalar masses arise from one-loop finite contributions as well as direct gravity-mediated contributions. Like split supersymmetry, one Higgs doublet is fine-tuned to be light. The scale at which the Dirac gauginos are introduced to make the Higgs quartic zero is the same as is necessary for gauge coupling unification. Thus, gauge coupling unification persists (nontrivially, due to adjoint multiplets), though with a somewhat higher unification scale $\gtrsim 10^{17}$ GeV. The $\mu$-term is naturally at the weak scale, and provides an opportunity for experimental verification. We present two manifestations of Split Dirac Supersymmetry. In the "Pure Dirac" model, the lightest Higgsino must decay through R-parity violating couplings, leading to an array of interesting signals in colliders. In the "Hypercharge Impure" model, the bino acquires a Majorana mass that is one-loop suppressed compared with the Dirac gluino and wino. This leads to weak scale Higgsino dark matter whose overall mass scale, as well as the mass splitting between the neutral components, is naturally generated from the same UV dynamics. We outline the challenges to discovering pseudo-Dirac Higgsino dark matter in collider and dark matter detection experiments.

Non-conformal limit of AGT relation from the 1-point torus conformal block

Given a 4d N=2 SUSY gauge theory, one can construct the Seiberg-Witten prepotentional, which involves a sum over instantons. Integrals over instanton moduli spaces require regularisation. For UV-finite theories the AGT conjecture favours particular, Nekrasov's way of regularization. It implies that Nekrasov's partition function equals conformal blocks in 2d theories with W_{N_c} chiral algebra. For $N_c=2$ and one adjoint multiplet it coincides with a torus 1-point Virasoro conformal block. We check the AGT relation between conformal dimension and adjoint multiplet's mass in this case and investigate the limit of the conformal block, which corresponds to the large mass limit of the 4d theory e.i. the asymptotically free 4d N=2 supersymmetric Yang-Mills theory. Though technically more involved, the limit is the same as in the case of fundamental multiplets, and this provides one more non-trivial check of AGT conjecture.

Supersymmetry breaking

AbstractI will describe a minimal supersymmetric SU(5) model, in which the adjoint multiplet breaks spontaneously both gauge and supersymmetry. This inevitably leads to intermediate scales, which in turn increase the GUT scale. The dimension 6 proton decay is thus suppressed, while soft terms coming from supergravity typically dominate.

SUSY BREAKING IN GUTS

I will describe a minimal supersymmetric SU(5) model, in which the adjoint multiplet breaks spontaneously both gauge and supersymmetry. This inevitably leads to intermediate scales, which in turn increase the GUT scale. The dimension 6 proton decay is thus suppressed, while soft terms coming from supergravity typically dominate.

Adjoint chiral supermultiplets and their phenomenology

Matter fields in the minimal supersymmetric standard model are chiral supermultiplets in fundamental (or singlet) representations of the standard model gauge group. In this paper we introduce chiral superfields in the adjoint representation of $SU(3{)}_{C}$ and study the effective field theory and phenomenology of them. These states are well motivated by intersecting D-brane models in which additional massless adjoint chiral supermultiplets appear generically in the low-energy spectrum. Although it has been pointed out that the existence of these additional fields may make it difficult to obtain asymptotic freedom, we demonstrate that this consideration does not rule out the existence of adjoints. The QCD gauge coupling can be perturbative up to a sufficiently high scale, and therefore a perturbative description for a D-brane model is valid. The full supersymmetric and soft SUSY breaking Lagrangians and the resulting renormalization group equations are given. Phenomenological aspects of the adjoint matter are also studied, including the decay and production processes. The similarity in gauge interaction between the adjoint fermion and gluino facilitates our study on these aspects. It is found that these adjoint multiplets can give detectable signals at colliders and satisfy the constraints from cosmology.

Deconfinement at the Argyres–Douglas point in SU(2) gauge theory with broken supersymmetry

We consider chiral condensates in SU(2) gauge theory with broken N =2 supersymmetry. The matter sector contains an adjoint multiplet and one fundamental flavor. Matter and gaugino condensates are determined by integrating out the adjoint field. The only nonperturbative input is the Affleck–Dine–Seiberg (ADS) superpotential generated by one instanton plus the Konishi anomaly. These results are consistent with those obtained by the `integrating in' procedure, including a reproduction of the Seiberg–Witten curve from the ADS superpotential. We then calculate monopole, dyon, and charge condensates using the Seiberg–Witten approach. We show that the monopole and charge condensates vanish at the Argyres–Douglas point where the monopole and charge vacua collide. We interpret this phenomenon as a deconfinement of electric and magnetic charges at the Argyres–Douglas point.

Equivalence between two-dimensional SU( n) QCD and Schwinger model: An analysis of strong coupling phase

The {U(1)} n Schwinger model is shown to have a hidden global SU( n) invariance where the fermion fields are coupled to n 2−1 vector fields forming the adjoint multiplet. Of these vector fields only n−1 are the gauge fields while the others are dependent degrees of freedom. This model, which is called SU( n) torus QCD, is shown, in the Coulomb gauge, to be equivalent to the full SU( n) QCD 2 in a fixed gauge where A 1, aa = 0 and A 1, ab = 0 for a ≠ b. All the gauge-invariant consequences of the two models are, therefore, the same. The quarks are topologically confined for any finite n. However, in the strong coupling phase the quarks are liberated in the limit n → ∞.