A natural composite Higgs via universal boundary conditions

We present a novel realization of a composite Higgs, which can naturally produce top partners above the current LHC bounds without increasing the tuning above 10%. The essential ingredients are softened breaking of the Higgs shift symmetry as well as maximal symmetry, which turn out to perfectly complement each other. The 5D realization of this model is particularly simple: universal UV and IR boundary conditions for the bulk fermions containing the SM fields will cure the problems of existing holographic composite Higgs models and provide a complete viable model for a naturally light Higgs without much tuning.

Naturalness without new particles

We demonstrate that the physics which resolves naturalness problems need not take the form of new particles and can sometimes manifest itself as higher dimensional operators. As a proof of principle, we present a simple model where the scale of new particles is parametrically separated from that estimated via naturalness arguments applied to self-quartic couplings. In this example, new particles appear far above the scale $$ m/\sqrt{\lambda } $$ m / λ , where m is the mass of the particle and λ is its self-quartic coupling. The shift symmetry responsible for resolving the naturalness problem involves higher dimensional operators rather than new particles.

The Batalin–Vilkovisky formalism description of self-dual Chern–Simons gauge theory coupled to matter fields in superspace

We construct the extended BRST and anti-BRST transformation by considering a shift symmetry both in Abelian and non-Abelian Chern–Simons theories coupled to scalar fields using the approach of Batalin–Vilkovisky quantization. The extended BRST invariant Lagrangian density is able to be addressed in the framework of superfield formalism with one fermionic coordinate. In the case of extended BRST–anti-BRST symmetry, it is shown that the Batalin–Vilkovisky action of the theory can be expressed in a covariant form with two fermionic coordinates in the superspace.

On the coupling of Galilean-invariant field theories to curved spacetime

We consider the problem of coupling Galilean-invariant quantum field theories to a fixed spacetime. We propose that to do so, one couples to Newton-Cartan geometry and in addition imposes a one-form shift symmetry. This additional symmetry imposes invariance under Galilean boosts, and its Ward identity equates particle number and momentum currents. We show that Newton-Cartan geometry subject to the shift symmetry arises in null reductions of Lorentzian manifolds, and so our proposal is realized for theories which are holographically dual to quantum gravity on Schrödinger spacetimes. We use this null reduction to efficiently form tensorial invariants under the boost and particle number symmetries. We also explore the coupling of Schrödinger-invariant field theories to spacetime, which we argue necessitates the Newton-Cartan analogue of Weyl invariance.