Inflation and supersymmetry breaking in Higgs-R2 supergravity

We propose a new construction of the supergravity inflation as an UV completion of the Higgs-R2 inflation. In the dual description of R2-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.

Nilpotent superfields for broken abelian symmetries

We find new solutions to real cubic constraints on $$N=1$$ N = 1 chiral superfields transforming under global abelian symmetries. These solutions describe the low-energy dynamics of a goldstino interacting with an axion (both belonging to the same chiral superfield) with non-linearly realized supersymmetry. We show the relation between our model and the approach of Komargodski and Seiberg for describing goldstino-axion dynamics which uses orthogonal nilpotent superfields.

Fusion of interfaces in Landau-Ginzburg models: a functorial approach

We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.

Proton decay in supersymmetric SU(4)c × SU(2)L × SU(2)R

We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry SU(4)c× SU(2)L× SU(2)R. A U(1) R symmetry plays an essential role in realizing inflation as well as in eliminating some undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include p → e+(μ+) + π0, $$ p\to \overline{\nu}+{\pi}^{+} $$ p → ν ¯ + π + , p → K0 + e+(μ+), and $$ p\to {K}^{+}+\overline{\nu} $$ p → K + + ν ¯ , with a lifetime estimate of order 1034–1036 yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale MGUT (∼ 1016 GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed.

A cubic deformation of ABJM: the squashed, stretched, warped, and perturbed gets invaded

A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new $$ \mathcal{N} $$ N = 2 superconformal phase. This is holographically dual to a warped AdS4×wS7 solution of M-theory equipped with a squashed and stretched metric on S7. We determine the spectrum of spin-2 operators of the cubic deformation at low energies by computing the spectrum of Kaluza-Klein (KK) gravitons over the dual AdS4 solution. We calculate, numerically, the complete graviton spectrum and, analytically, the spectrum of gravitons that belong to short multiplets. We also use group theory to assess the structure of the full KK spectrum, and conclude that $$ \mathcal{N} $$ N = 2 supermultiplets cannot be allocated KK level by KK level. This phenomenon, usually referred to as “space invaders scenario”, is also known to occur for another AdS4 solution based on a different squashed S7.

Twisted characters and holomorphic symmetries

We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly as a family over the space of nilpotent supercharges in minimal supersymmetry. The BV formalism allows one to work with or without auxiliary fields, according to preference; for chiral superfields, we show that the result of the twist is an identical BV theory, the holomorphic $$\beta \gamma $$ β γ system with superpotential, independent of whether or not auxiliary fields are included. We compute the character of local operators in this holomorphic theory, demonstrating agreement of the free local operators with the usual index of free fields. The local operators with superpotential are computed via a spectral sequence and are shown to agree with functions on a formal mapping space into the derived critical locus of the superpotential. We consider the holomorphic theory on various geometries, including Hopf manifolds and products of arbitrary pairs of Riemann surfaces, and offer some general remarks on dimensional reductions of holomorphic theories along the $$(n-1)$$ ( n - 1 ) -sphere to topological quantum mechanics. We also study an infinite-dimensional enhancement of the flavor symmetry in this example, to a recently studied central extension of the derived holomorphic functions with values in the original Lie algebra, that generalizes the familiar Kac–Moody enhancement in two-dimensional chiral theories.

New Kähler invariant Fayet–Iliopoulos terms in supergravity and cosmological applications

Recently, a new type of constant Fayet–Iliopoulos (FI) terms was introduced in $${\mathcal {N}}=1$$ N = 1 supergravity, which do not require the gauging of the R-symmetry. We revisit and generalise these constructions, building a new class of Kähler invariant FI terms parametrised by a function of the gravitino mass as functional of the chiral superfields, which is then used to describe new models of inflation. They are based on a no-scale supergravity model of the inflaton chiral multiplet, supplemented by an abelian vector multiplet with the new FI-term. We show that the inflaton potential is compatible with the CMB observational data, with a vacuum energy at the minimum that can be tuned to a tiny positive value. Finally, the axionic shift symmetry can be gauged by the U(1) which becomes massive. These models offer a mechanism for fixing the gravitino mass in no-scale supergravities, that corresponds to a flat direction of the scalar potential in the absence of the new FI-term; its origin in string theory is an interesting open problem.