Interaction of anomaly-induced gravity with quantized matter and temperature effects

In this dissertation we investigate aspects of the UV completion of the Standard Model of particle physics. We focus on two examples that inevitably require new degrees of freedom: baryon asymmetry and quantum gravity. Baryogenesis can occur at the electroweak phase transition if new physics triggers the phase transition to be of strong first order. We consider generic classes of beyond the Standard Model physics and show that all of them give rise to a strongly enhanced Higgs self-coupling if we demand electroweak baryogenesis. The Higgs self-coupling will be measured precisely enough in the high-luminosity run of the LHC. Quantum gravity is investigated with the asymptotic safety approach, which conjectures the existence of a UV fixed point of the renormalisation group flow. The latter allows for a non-perturbative renormalisation of quantum gravity. We develop the approach towards quantitative precision by systematically computing flows of higher-order correlation functions. We start from a minimal setup that includes a genuine Newton's coupling, which is the setup with the graviton two- and three-point function. In a first extension we include the graviton four-point function, which allows to investigate convergence properties and the restoration of diffeomorphism symmetry in the IR. In a second extension we evaluate the correlation functions on a constantly-curved background. From this we set up the equations of motion and find a solution at negative background curvature. Overall, these results add further significant evidence for the existence of the UV fixed point. We include Standard Model matter content into the quantum gravity setup. We start with minimally coupled scalars and fermions and subsequently also couple Yang-Mills theory to quantum gravity. We provide a formal argument that such systems must be compatible with asymptotic safety independent of the number of gauge or matter fields. Furthermore we show an effective universality between different avatars of Newton's coupling, which means that their flows are in quantitative agreement in the scaling region of the UV fixed point. These results are the basis for future investigations of the Standard Model fully coupled to quantum gravity.

The standard theory of metals, Fermi liquid theory, hinges on the key assumption that although the electrons interact, the low-energy excitation spectrum stands in a one-to-one correspondence with that of a non-interacting system. In the normal state of the copper-oxide high-temperature superconductors, drastic deviations from the Fermi liquid picture are obtained, highlighted by a pseudogap, broad spectral features and T-linear resistivity. A successful theory in this context must confront the highly constraining scaling argument which establishes that all 4-Fermi interactions are irrelevant (except for pairing) at a Fermi surface. This argument lays plain that new low-energy degrees of freedom are necessary. This paper focuses on the series of experiments on copper-oxide superconductors which reveal that the number of low-energy addition states per electron per spin exceeds unity, in direct violation of the key Fermi liquid tenet. These experiments point to new degrees of freedom, not made out of the elemental excitations, as the key mechanism by which Fermi liquid theory breaks down in the cuprates. A recent theoretical advance which permits an explicit integration of the high-energy scale in the standard model for the cuprates reveals the source of the new dynamical degrees of freedom at low energies, a charge 2e bosonic field which has nothing to do with pairing but rather represents the mixing with the high-energy scales. We demonstrate explicitly that at half-filling, this new degree of freedom provides a dynamical mechanism for the generation of the charge gap and antiferromagnetism in the insulating phase. At finite doping, many of the anomalies of the normal state of the cuprates including the pseudogap, T-linear resistivity and the mid-infrared band are reproduced. A possible route to superconductivity is explored.

Thermodynamic metric usually works only for those black holes with more than one conserved charge, thereby excluding the Schwarzschild black hole. In this paper, however, different versions of thermodynamic metric are computed and compared for the Schwarzschild-like black hole by introducing new degrees of freedom. These new degrees of freedom have two purposes. First, the deformed metric may be treated offshell to the ordinary Schwarzschild black hole, and onshell physics corresponds to the submanifold by gauge fixing of this additional degree of freedom. In particular, the thermal Ricci scalar for the Schwarzschild black hole, though different for various deformations, can be obtained by switching off the deformation. Second, while deformed metric is treated onshell, a divergent Ricci scalar may signal an exotic phase in which new physical degrees of freedom manifest. This paper considers the new degree of freedom as the running Newton constant, a cutoff scale for regular black holes, a noncommutative deformation or the deformed parameter in the nonextensive Tsallis–Rènyi entropy.

At high energy scale the only quantum effect of any asymptotic free and asymptotically conformal invariant GUT is the trace anomaly of the energy-momentum tensor. Anomaly generates the new degree of freedom, that is propagating conformal factor. At lower energies conformal factor starts to interact with scalar field because of the violation of conformal invariance. We estimate the effect of such an interaction and find the running of the nonminimal coupling from conformal value $\frac{1}{6}$ to $0$. Then we discuss the possibility of the first order phase transition induced by curvature in a region close to the stable fixed point and calculate the induced values of Newtonian and cosmological constants.

Pure R2 gravity (R2 gravity by itself with no Einstein-Hilbert term) has attracted attention because it is different from other quadratic gravity theories. In a curved de Sitter (dS) or anti-de Sitter (AdS) background, it is equivalent to Einstein gravity with an additional massless scalar and with a cosmological constant. In contrast to other higher-derivative theories, it is therefore unitary. The equivalence with Einstein gravity is not valid for a flat background. In fact, it has been shown that linearizations of pure R2 gravity about flat spacetime does not produce a graviton. In other words, it does not gravitate about flat space. Pure R2 gravity is invariant under restricted Weyl transformations where the metric is scaled by a conformal factor that obeys a harmonic condition. In this work we consider an action composed of pure R2 gravity, a massless scalar field φ non-minimally coupled to gravity plus other terms. The entire action is invariant under restricted Weyl transformations. We show that when the scalar field φ acquires a non-zero vacuum expectation value (VEV), flat spacetime now becomes a viable gravitating background solution. The restricted Weyl symmetry becomes broken, not explicitly but spontaneously. In other words, when φ acquires a non-zero VEV, the equivalent Einstein action has now the possibility of having a zero cosmological constant and therefore solutions in a Minkowski background. The action can also have, as before, a non-zero cosmological constant, so that solutions in a dS and AdS background are still possible.

Relying only on the standard model of elementary particles and gravity, we study the details of a new source of gravitational waves whose origin is in quantum physics. Namely, it is well known that massless fields in curved backgrounds suffer from the so-called ‘trace anomaly’. This anomaly can be cast in terms of new scalar degrees of freedom which take account of macroscopic effects of quantum matter in gravitational fields. The linearized effective action for these fields describes scalar (as opposed to transverse) gravitational waves, which are absent in Einstein’s theory. Since these new degrees of freedom couple directly to the gauge field scalars in QCD, the epoch of the QCD phase transition in early universe is a possible source of primordial cosmological gravitational radiation. While the anomaly is most likely fully unsuppressed at the QCD densities (temperature is much higher than the u and d quark masses), just to be careful we introduced the window function which cuts-off very low frequencies where the anomaly effect might be suppressed. We then calculated the characteristic strain of the properly adjusted gravitational waves signal today. The region of the parameter space with no window function gives a stronger signal, and both the strain and the frequencies fall within the sensitivity of the near future gravitational wave experiments (e.g. LISA and The Big Bang Observer). The possibility that one can study quantum physics with gravitational wave astronomy even in principle is exciting, and will be of value for future endeavors in this field.

The making of an intrinsic property: “Symmetry heuristics” in early particle physics

The enigmatic properties of quarks have been described by introducing for them a new SU(3) degree of freedom, which is an exact symmetry+, with the additional constraint that only states scalar under this new group, named SUc(3) to distinguisgh it from the SU(3) of isospin and strangeness, can be observed(2). This assumption implies that quarks, which transform under SUc(3) as the fundamental representation, cannot be observed alone but only in pairs qq (mesons) or in triplets (baryons). This new degree of freedom accounts for the symmetry in the others quantum numbers of the baryon wave function and succesfully explains (π0→2x) or reduces OR value) previous discrepancies. The main purpose of this talk is to show that the octonion algebra supplies a natural framework both for the SU(3) character of the new degree of freedom and for the non observability of non singlet states(3).

What are the key degrees of freedom for the next generation of quantum functional materials?

The idea of quark-lepton universality at high energies has been introduced as a natural extension to the standard model. This is achieved by endowing leptons with new degrees of freedom---leptonic color, an analogue of the familiar quark color. Grand and partially unified models which utilize this new gauge symmetry $SU(3{)}_{\ensuremath{\ell}}$ have been proposed in the context of the quartification gauge group $SU(3{)}^{4}$. Phenomenologically successful gauge coupling constant unification without supersymmetry has been demonstrated for cases where the symmetry breaking leaves a residual $SU(2{)}_{\ensuremath{\ell}}$ unbroken. Though attractive, these schemes either incorporate ad hoc discrete symmetries and nonrenormalizable mass terms, or achieve only partial unification. We show that grand unified models can be constructed where the quartification group can be broken fully [i.e. no residual $SU(2{)}_{\ensuremath{\ell}}$] to the standard model gauge group without requiring additional discrete symmetries or higher dimension operators. These models also automatically have suppressed nonzero neutrino masses. We perform a systematic analysis of the renormalization-group equations for all possible symmetry breaking routes from $SU(3{)}^{4}\ensuremath{\rightarrow}SU(3{)}_{q}\ensuremath{\bigotimes}SU(2{)}_{L}\ensuremath{\bigotimes}U(1{)}_{Y}$. This analysis indicates that gauge coupling unification can be achieved for several different symmetry breaking patterns and we outline the requirements that each gives on the unification scale. We also show that the unification scenarios of those models which leave a residual $SU(2{)}_{\ensuremath{\ell}}$ symmetry are not unique. In both symmetry breaking cases, some of the scenarios require new physics at the TeV scale, while others do not allow for new TeV phenomenology in the fermionic sector.

The idea of quark-lepton universality at high energies has been introduced as a natural extension to the standard model. This is achieved by endowing leptons with new degrees of freedom -- leptonic colour, an analogue of the familiar quark colour. Grand and partially unified models which utilise this new gauge symmetry SU(3)_\ell have been proposed in the context of the quartification gauge group SU(3)^4. Phenomenologically successful gauge coupling constant unification without supersymmetry has been demonstrated for cases where the symmetry breaking leaves a residual SU(2)_\ell unbroken. Though attractive, these schemes either incorporate ad hoc discrete symmetries and non-renormalisable mass terms, or achieve only partial unification. We show that grand unified models can be constructed where the quartification group can be broken fully [i.e. no residual SU(2)_\ell] to the standard model gauge group without requiring additional discrete symmetries or higher dimension operators. These models also automatically have suppressed nonzero neutrino masses. We perform a systematic analysis of the renormalisation-group equations for all possible symmetry breaking routes from SU(3)^4 --> SU(3)_q x SU(2)_L x U(1)_Y. This analysis indicates that gauge coupling unification can be achieved for several different symmetry breaking patterns and we outline the requirements that each gives on the unification scale. We also show that the unification scenarios of those models which leave a residual SU(2)_\ell symmetry are not unique. In both symmetry breaking cases, some of the scenarios require new physics at the TeV scale, while others do not allow for new TeV phenomenology in the fermionic sector.

Despite the success of general relativity in explaining classical gravitational phenomena, several problems at the interface between gravitation and high energy physics remain open to date. The purpose of this thesis is to explore classical and quantum gravity in order to improve our understanding of different aspects of gravity, such as dark matter, gravitational waves and ination. We focus on the class of higher derivative gravity theories as they naturally arise after the quantization of general relativity in the framework of effective field theory. The inclusion of higher order curvature invariants to the action always come in the form of new degrees of freedom. From this perspective, we introduce a new formalism to classify gravitational theories based on their degrees of freedom and, in light of this classification, we argue that dark matter is no different from modified gravity. Additional degrees of freedom appearing in the quantum gravitational action also affect the behaviour of gravitational waves. We show that gravitational waves are damped due to quantum degrees of freedom and we investigate the backreaction of these modes. The implications for gravitational wave events, such as the ones recently observed by the Advanced LIGO collaboration, are also discussed. The early universe can also be studied in this framework. We show how ination can be accommodated in this formalism via the generation of the Ricci scalar squared, which is triggered by quantum effects due to the non-minimal coupling of the Higgs boson to gravity, avoiding instability issues associated with Higgs ination. We argue that the non-minimal coupling of the Higgs to the curvature could also solve the vacuum instability issue by producing a large effective mass for the Higgs, which quickly drives the Higgs field back to the electroweak vacuum during ination.

We present an exact solution to the equations of massive gravity that displays cosmological constant-like behavior for any spherically symmetric distribution of matter, including arbitrary time dependence. On this solution, the new degrees of freedom from the massive graviton generate a cosmological constant-like contribution to stress-energy that does not interact directly with other matter sources. When the effective cosmological constant contribution dominates over other sources of stress energy the cosmological expansion self-accelerates, even when no other dark-energy-like ingredients are present. The new degrees of freedom introduced by giving the graviton the mass do not respond to arbitrarily large radial or homogeneous perturbations from other matter fields on this solution. We comment on possible implications of this result.

In this paper, we consider finite-temperature holographic renormalization group (RG) flows in D=3 N=(2,0) gauged truncated supergravity coupled to a sigma model with a hyperbolic target space. In the context of the holographic duality, fixed points (CFTs) at finite temperature are described by anti–de Sitter (AdS) black holes. We come from the gravity equations of motion to a 3D autonomous dynamical system, which critical points can be related to fixed points of dual field theories. Near-horizon black hole solutions correspond to infinite points of this system. We use Poincaré transformations to project the system on R3 into the 3D unit cylinder such that the infinite points are mapped onto the boundary of the cylinder. We explore numerically the space of solutions. We show that the exact RG flow at zero temperature is the separatrix for asymptotically AdS black hole solutions if the potential has one extremum, while for the potential with three extrema the separatrices are RG flows between AdS fixed points. We find near-horizon analytical solutions for asymptotically AdS black holes using the dynamical equations. We also present a method for constructing full analytical solutions. Published by the American Physical Society 2024

We analyze the quantum process in which a cosmic string breaks in an anti-de Sitter (AdS) background, and a pair of charged or neutral black holes is produced at the ends of the strings. The energy to materialize and accelerate the pair comes from the strings tension. In an AdS background this is the only study done in the process of production of a pair of correlated black holes with spherical topology. The acceleration $A$ of the produced black holes is necessarily greater than (|L|/3)^(1/2), where L<0 is the cosmological constant. Only in this case the virtual pair of black holes can overcome the attractive background AdS potential well and become real. The instantons that describe this process are constructed through the analytical continuation of the AdS C-metric. Then, we explicitly compute the pair creation rate of the process, and we verify that (as occurs with pair creation in other backgrounds) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of exp(Area/4), where Area is the black hole horizon area. We also conclude that the general behavior of the pair creation rate with the mass and acceleration of the black holes is similar in the AdS, flat and de Sitter cases, and our AdS results reduce to the ones of the flat case when L=0.