# Open Access Repository

### Non-perturbative fixed points and renormalization group improved effective potential

The stability conditions of a renormalization group improved effective potential have been discussed in the case of scalar QED and QCD with a colorless scalar. We calculate the same potential in these models assuming the existence of non-perturbative fixed points associated with a conformal phase. In the case of scalar QED the barrier of instability found previously is barely displaced as we approach the fixed point, and in the case of QCD with a colorless scalar not only the barrier is changed but the local minimum of the potential is also changed

### Scale-invariance as the origin of dark radiation?

Recent cosmological data favor R2 -inflation and some amount of non-standard dark radiation in the Universe. We show that a framework of high energy scale invariance can explain these data. The spontaneous breaking of this symmetry provides gravity with the Planck mass and particle physics with the electroweak scale. We found that the corresponding massless Nambu–Goldstone bosons – dilatons – are produced at reheating by the inflaton decay right at the amount needed to explain primordial abundances of light chemical elements and anisotropy of the cosmic microwave background. Then we extended the discussion on the interplay with Higgs-inflation and on general class of inflationary models where dilatons are allowed and may form the dark radiation. As a result we put a lower limit on the reheating temperature in a general scale invariant model of inflation

### Global and local properties of AdS 2 higher spin gravity

Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS 2 higher spin gravity model describing a consistent interaction between local fields in AdS 2 space including gravitational field, higher spin partially-massless fields, and dilaton fields. We carry out analysis of the frame-like and the metric-like formulation of the theory. Infinite-dimensional higher spin global algebras and their finite-dimensional truncations are realized in terms of o (2 , 1) − sp (2) Howe dual auxiliary variables

### Spherically Symmetric Solution in (1+4)-Dimensional <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo>[/itex] Gravity Theories

A nondiagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate <math id="M2" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>r</mi></mrow>[/itex] plus an angle <math id="M3" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Φ</mi></mrow>[/itex] , which is a generalization of the azimuthal angle <math id="M4" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ϕ</mi></mrow>[/itex] , is applied to the field equations of (1+4)-dimensional <math id="M5" xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo>[/itex] gravity theory. A special vacuum solution with one constant of integration is derived. The physical meaning of this constant is shown to be related to the gravitational mass of the system and the associated metric represents Schwarzschild in (1+4)-dimension. The scalar torsion related to this solution vanishes. We put the derived solution in a matrix form and rewrite it as a product of three matrices: the first represents a rotation while the second represents an inertia and the third matrix is the diagonal square root of Schwarzschild spacetime in (1+4)-dimension

### Emergent spacetime in stochastically evolving dimensions

Changing the dimensionality of the space–time at the smallest and largest distances has manifold theoretical advantages. If the space is lower dimensional in the high energy regime, then there are no ultraviolet divergencies in field theories, it is possible to quantize gravity, and the theory of matter plus gravity is free of divergencies or renormalizable. If the space is higher dimensional at cosmological scales, then some cosmological problems (including the cosmological constant problem) can be attacked from a completely new perspective. In this paper, we construct an explicit model of “evolving dimensions” in which the dimensions open up as the temperature of the universe drops. We adopt the string theory framework in which the dimensions are fields that live on the string worldsheet, and add temperature dependent mass terms for them. At the Big Bang, all the dimensions are very heavy and are not excited. As the universe cools down, dimensions open up one by one. Thus, the dimensionality of the space we live in depends on the energy or temperature that we are probing. In particular, we provide a kinematic Brandenberger–Vafa argument for how a discrete causal set, and eventually a continuum (3+1) -dim spacetime along with Einstein gravity emerges in the Infrared from the worldsheet action. The (3+1) -dim Planck mass and the string scale become directly related, without any compactification. Amongst other predictions, we argue that LHC might be blind to new physics even if it comes at the TeV scale. In contrast, cosmic ray experiments, especially those that can register the very beginning of the shower, and collisions with high multiplicity and density of particles, might be sensitive to the dimensional cross-over

### Monojet versus the rest of the world I: t -channel models

Monojet searches using Effective Field Theory (EFT) operators are usually interpreted as a robust and model independent constraint on direct detection (DD) scattering cross-sections. At the same time, a mediator particle must be present to produce the dark matter (DM) at the LHC. This mediator particle may be produced on shell, so that direct searches for the mediating particle can constrain the effective operator being applied to monojet constraints. In this first paper, we do a case study on t -channel models in monojet searches, where the (Standard Model singlet) DM is pair produced via a t -channel mediating particle, whose supersymmetric analogue is the squark. We compare monojet constraints to direct constraints on single or pair production of the mediator from multi-jets plus missing energy searches and we identify the regions where the latter dominate over the former. We show that computing bounds using supersymmetric simplified models and in the narrow width approximation, as done in previous work in the literature, misses important quantitative effects. We perform a full event simulation and statistical analysis, and we compute the effects of both on- and off-shell production of the mediating particle, showing that for both the monojet and multi-jets plus missing energy searches, previously derived bounds provided more conservative bounds than what can be extracted by including all relevant processes in the simulation. Monojets and searches for super-symmetry (SUSY) provide comparable bounds on a wide range of the parameter space, with SUSY searches usually providing stronger bounds, except in the regions where the DM particle and the mediator are very mass degenerate. The EFT approximation rarely is able to reproduce the actual limits. In a second paper to follow, we consider the case of s -channel mediators

### Strong phase transition, dark matter and vacuum stability from simple hidden sectors

Motivated by the possibility to explain dark matter abundance and strong electroweak phase transition, we consider simple extensions of the Standard Model containing singlet fields coupled with the Standard Model via a scalar portal. Concretely, we consider a basic portal model consisting of a singlet scalar with Z2 symmetry and a model containing a singlet fermion connected with the Standard Model fields via a singlet scalar portal. We perform a Monte Carlo analysis of the parameter space of each model, and we find that in both cases the dark matter abundance can be produced either via freeze-out or freeze-in mechanisms, but only in the latter model one can obtain also a strong electroweak phase transition required by the successful electroweak baryogenesis. We impose the direct search limits and consider systematically the possibility that the model produces only a subdominant portion of the dark matter abundance. We also study the renormalization group evolution of the couplings of the model to determine if the scalar sector of the model remains stable and perturbative up to high scales. With explicit examples of benchmark values of the couplings at weak scale, we show that this is possible. Models of this type are further motivated by the possibility that the excursions of the Higgs field at the end of inflation are large and could directly probe the instability region of the Standard Model

### Probing quarkonium production mechanisms with jet substructure

We use fragmenting jet functions (FJFs) in the context of quarkonia to study the production channels predicted by NRQCD ( 3 S 1 (1) ,  3 S 1 (8) ,  1 S 0 (8) ,  3 P J (8) ). We choose a set of FJFs that give the probability to find a quarkonium with a given momentum fraction inside a cone-algorithm jet with fixed cone size and energy. This observable gives several lever arms that allow one to distinguish different production channels. In particular, we show that at fixed momentum fraction the individual production mechanisms have distinct behaviors as a function of the the jet energy. As a consequence of this fact, we arrive at the robust prediction that if the depolarizing 1 S 0 (8) matrix element dominates, then the gluon FJF will diminish with increasing energy for fixed momentum fraction, z , and z > 0.5

### Charged Rényi entropies in CFTs with Einstein-Gauss-Bonnet holographic duals

We calculate the Rényi entropy S q ( μ, λ ), for spherical entangling surfaces in CFT’s with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings λ , larger than specific value, but still allowed by causality, we observe a violation of the inequality ∂ ∂ q q − 1 q S q μ λ ≥ 0 $$\frac{\partial }{\partial q}\left(\frac{q-1}{q}{S}_q\left(\mu, \lambda \right)\right)\ge\ 0$$ , which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of S q ( μ, λ ) for imaginary chemical potential, between negative and non-negative λ

### On KP-integrable Hurwitz functions

There is now a renewed interest [1]–[4] to a Hurwitz τ -function, counting the isomorphism classes of Belyi pairs, arising in the study of equilateral triangulations and Grothiendicks’s dessins d ’ enfant . It is distinguished by belonging to a particular family of Hurwitz τ -functions, possessing conventional Toda/KP integrability properties. We explain how the variety of recent observations about this function fits into the general theory of matrix model τ -functions. All such quantities possess a number of different descriptions, related in a standard way: these include Toda/KP integrability, several kinds of W -representations (we describe four), two kinds of integral (multi-matrix model) descriptions (of Hermitian and Kontsevich types), Virasoro constraints, character expansion, embedding into generic set of Hurwitz τ -functions and relation to knot theory. When approached in this way, the family of models in the literature has a natural extension, and additional integrability with respect to associated new time-variables. Another member of this extended family is the Itsykson-Zuber integral
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