Quantum error correction and large $N$

In recent years quantum error correction (QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large NN theories. Specifically we examine SU(N)SU(N) matrix quantum mechanics and 3-rank tensor O(N)^3O(N)3 theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large NN analysis and do not appeal to a particular form of Hamiltonian or holography.

Cosmological constant, axial anomalies and photon mass dynamos from chiral Fermionic torsion

Motivated by Palle’s investigation on the handness of chirality of vorticity in Einstein–Cartan cosmology [Entropy 5 (2014)], several aspects of chiral torsional handness in magnetogenesis and cosmology are presented. In the first one, we obtain torsion bounds from massive photons and axial anomalies. In the second, we deal with magnetogenesis from photon mass and in the third, we discuss chiral torsion degrees of freedom to obtain a torsion cosmological constant dependent solution. The torsion solution decays fast and implies a strong suppression of torsion at present universe. Our result contains the Poplawski [Phys. Lett. B (2010)] results in the case axial torsion vector associated to Einstein–Cartan fermionic sector matter and conformal anomalies of quarks. In the third example, a magnetic field bound from chiral torsionic dynamos is obtained as [Formula: see text]. In the non-minimal cosmological models, chiral dynamos are sourced by massive photons, London currents and chiral magnetic effect (CME). Chiral chemical potential is found to be mimic by torsion. Cosmological constant bound [Formula: see text] is found. At the early universe, the cosmological constant [Formula: see text] is obtained. Torsion used in the present universe is [Formula: see text]. In the last and fourth example, chiral anisotropic currents are obtained and magnetic helicity is shown to depend upon torsion when the chiral chemical potential is non-constant.

$$\alpha $$-attractors from supersymmetry breaking

We construct new models of inflation and spontaneous supersymmetry breaking in de Sitter vacuum, with a single chiral superfield, where inflaton is the superpartner of the goldstino. Our approach is based on hyperbolic Kähler geometry, and a gauged (non-axionic) $$U(1)_R$$ U ( 1 ) R symmetry rotating the chiral scalar field by a phase. The $$U(1)_R$$ U ( 1 ) R gauge field combines with the angular component of the chiral scalar to form a massive vector, and single-field inflation is driven by the radial part of the scalar. We find that in a certain parameter range they can be approximated by simplest Starobinsky-like (E-model) $$\alpha $$ α -attractors, thus predicting $$n_s$$ n s and r within $$1\sigma $$ 1 σ CMB constraints. Supersymmetry (and R-symmetry) is broken at a high scale with the gravitino mass $$m_{3/2} > rsim 10^{14}$$ m 3 / 2 ≳ 10 14 GeV, and the fermionic sector also includes a heavy spin-1/2 field. In all the considered cases the inflaton is the lightest field of the model.

Symmetries and stabilisers in modular invariant flavour models

The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries ΓN and for a given element γ ∈ ΓN, we present an algorithm for finding stabilisers (specific values for moduli fields τγ which remain unchanged under the action associated to γ). We then employ this algorithm to find all stabilisers for each element of finite modular groups for N = 2 to 5, namely, Γ2 ≃ S3, Γ3 ≃ A4, Γ4 ≃ S4 and Γ5 ≃ A5. These stabilisers then leave preserved a specific cyclic subgroup of ΓN. This is of interest to build models of fermionic mixing where each fermionic sector preserves a separate residual symmetry.

Non-Abelian strings in N = 1 supersymmetric QCD

Non-Abelian flux tubes (strings) are well studied in N = 2 supersymmetric QCD in (3+1) dimensions. In addition to translational zero modes they have also orientational moduli associated with rotations of their fluxes inside a non- Abelian group. The dynamics of the orientational moduli is described by the two dimensional CP(N - 1) model living on the world sheet of the non-Abelian string. In this paper we consider a deformation of N = 2 supersymmetric QCD with the U(N) gauge group and Nf = N quark flavors with a mass term μ of the adjoint matter. In the limit of large μ the theory flows to an N = 1 supersymmetric QCD. We study the solution for the non-Abelian string in this limit and derive an effective theory on the string world sheet. The bosonic sector of this theory is still given by the CP(N -1) model. We study also the fermionic sector of the world sheet theory. Upon the deformation the non-Abelian string is no longer BPS and we show that the fermionic superorientational zero modes are all lifted. This leaves us with the pure bosonic CP(N-1) model on the string world sheet in the limit of N = 1 QCD. We discuss what happens to confined monopoles at large μ.

Flavour physics and extra-dimensions

Randall-Sundrum (RS) model of warped extra-dimensions were originally proposed to explain the Planck-weak scale hierarchy. It was soon realised that modifications of the original setup, by introducing the fields in the bulk, has several interesting features. In particular it imbues a rich flavour structure to the fermionic sector thereby offering an understanding of the Yukawa hierarchy problem. This construction is also useful in explaining the recently observed deviations in the decay of the B mesons. We consider two scenarios to this effect : A) Right handed muon fields coupled more to NP that the corresponding muon doublets (unorthodox case). Non-universality exists in the right handed sector. B) Standard scenario with anomalies explained primarily by non-universal couplings to the lepton doublets. Further, we establish correlation with the parameter space consistent with the flavour anomalies in the neutral current sector and obtain predictions for rare K- decay which are likely to be another candle for NP with increased precision. The prediction for rare K- decays are different according to the scenario, thereby serving as a useful discriminatory tool. We also discussthe large flavour violation in the lepton sector and present an example with the implementation of bulk leptonic MFV which is essential to realize the model with low KK scales. Further we consider a radical solution, called GUT RS models, where the RS geometry can work as theory of flavour in the absence of flavour symmetries. In this case the low energy brane corresponds to the GUT scale as a result of which RS is no longer solution to the gauge hierarchy problem. The Kaluza Klein (KK) modes in this setup are naturally heavy due to which the low energy constraints can be easily avoided. We use this framework to discuss the supersymmetric version of the RS model and provide means to test this scenario by considering rare lepton decays like τ → μγ.

Induction of the Lorentz-violating effective actions in quantum electrodynamics

We introduce a Lorentz-symmetry violating extended quantum electrodynamics (QED) which preserves gauge symmetry. The extended fermionic sector can radiatively induce an extended effective action which simultaneously displays the same electromagnetic terms present in the Carroll–Field–Jackiw, Myers–Pospelov and Aether actions.

Casimir operator dependences of nonperturbative fermionic QCD amplitudes

In eikonal and quenched approximations, it is argued that the strong coupling fermionic QCD Green’s functions and related amplitudes depart from a sole dependence on the [Formula: see text] quadratic Casimir operator, [Formula: see text], evaluated over the fundamental gauge group representation. Noted in nonrelativistic quark models and in a nonperturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other nonperturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie algebra of [Formula: see text]. Though numerically subleading effects, cubic Casimir dependences, here and elsewhere, appear to be a signature of the nonperturbative fermionic sector of QCD.

Nonlocal quantum field theory without acausality and nonunitarity at quantum level: Is SUSY the key?

The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality is expected to reappear at one loop. We suggest that the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e. by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory. An infinite number of divergent diagrams cancel each other by virtue of the nonrenormalization theorem of supersymmetry. However, supersymmetry is not enough to protect a theory from all acausal divergences. For instance, acausal contributions to supersymmetric corrections to D-terms are not protected by supersymmetry. On the other hand, we show in detail how supersymmetry also helps in dealing with D-terms: divergences are not canceled but they become softer than in the nonsupersymmetric case. The supergraphs' formalism turns out to be a powerful tool to reduce the complexity of perturbative calculations.

Coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model

We discuss the coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model to study supersymmetry breaking for these fermions. We find that the coupled model has two distinct solutions. The first solution represents a local minimum of the superpotential which spontaneously breaks supersymmetry in perfect analogy to the O'Raifeartaigh model. The second solution is more intriguing as it corresponds to a global minimum of the superpotential. In this case, the coupling to the fermionic sector restores supersymmetry. However, this is achieved at the cost of breaking Lorentz invariance. Finally, the mass matrices for the multiplets of the coupled model are presented. It turns out that it contains two bosonic triplets and one fermionic doublet which are mass multiplets. In addition, it contains a massless fermionic doublet as well as one fermionic triplet which is not a mass multiplet but rather an interaction multiplet that contains component fields of different mass dimension. The results also imply that the presented model for fermionic fields with mass dimension one is an interesting candidate for supersymmetric dark matter (DM).