Non-trivial Renormalization Group Research Articles

A post-Gaussian approach to dipole symmetries and interacting fractons

We use a post-Gaussian variational approach to non-perturbatively study a general class of interacting bosonic quantum field theories with generalized dipole symmetries and fractonic behavior. We find that while a Gaussian approach allows to carry out a consistent renormalization group (RG) flow analysis of these theories, this only grasps the interaction terms associated with the longitudinal motion of dipoles, which is consistent with previous analysis using large N techniques. Remarkably, our post-Gaussian proposal, by providing a variational improved effective potential, can capture the transverse part of the interaction between dipoles in such a way that a non-trivial RG flow for this term is obtained and analyzed. Our results suggest that dipole symmetries that manifest due to the strong coupling of dipoles, may robustly emerge at low energies from short-distance models without that symmetry.

New conformal field theories by gauging electric and magnetic currents

Old folklore says that there is no nontrivial renormalization group fixed point with [Formula: see text] gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially infinitely many) novel types of field theories with [Formula: see text] gauge symmetry by gauging [Formula: see text] global symmetry electrically and magnetically. If the construction is consistent, the resulting theory will most likely possess a nontrivial renormalization group fixed point for the [Formula: see text] gauge coupling constant and it will be a nontrivial conformal field theory without the [Formula: see text] global symmetry in the infrared upon tunings of other relevant deformations. If the construction is CP-violating, a renormalization of the [Formula: see text]-parameter is accompanied.

Renormalization group flows for track function moments

Track functions describe the collective effect of the fragmentation of quarks and gluons into charged hadrons, making them a key ingredient for jet substructure measurements at hadron colliders, where track-based measurements offer superior angular resolution. The first moment of the track function, describing the average energy deposited in charged particles, is a simple and well-studied object. However, measurements of higher-point correlations of energy flow necessitate a characterization of fluctuations in the hadronization process, described theoretically by higher moments of the track function. In this paper we derive the structure of the renormalization group (RG) evolution equations for track function moments. We show that energy conservation gives rise to a shift symmetry that allows the evolution equations to be written in terms of cumulants, κ(N), and the difference between the first moment of quark and gluon track functions, ∆. The uniqueness of the first three cumulants then fixes their all-order evolution to be DGLAP, up to corrections involving powers of ∆, that are numerically suppressed by an effective order in the perturbative expansion for phenomenological track functions. However, at the fourth cumulant and beyond there is non-trivial RG mixing into products of cumulants such as κ(4) into κ(2)2. We analytically compute the evolution equations up to the sixth moment at mathcal{O} ( {alpha}_s^2 ), and study the associated RG flows. These results allow for the study of up to six-point correlations in energy flow using tracks, paving the way for precision jet substructure at the LHC.

The sinh-Gordon model beyond the self dual point and the freezing transition in disordered systems

The S-matrix of the well-studied sinh-Gordon model possesses a remarkable strong/weak coupling duality b → 1/b. Since there is no understanding nor evidence for such a duality based on the quantum action of the model, it should be questioned whether the properties of the model for b > 1 are simply obtained by analytic continuation of the weak coupling regime 0 < b < 1. In this article we assert that the answer is no, and we develop a concrete and specific proposal for the properties when b > 1. Namely, we propose that in this region one needs to introduce a background charge Q∞ = b + 1/b − 2 which differs from the Liouville background charge by the shift of −2. We propose that in this regime the model has non-trivial massless renormalization group flows between two different conformal field theories. This is in contrast to the weak coupling regime which is a theory of a single massive particle. Evidence for our proposal comes from higher order beta functions. We show how our proposal correctly reproduces the freezing transitions in the multi-fractal exponents of a Dirac fermion in 2 + 1 dimensions in a random magnetic field, which provides a strong check since such transitions have several detailed features. We also point out a connection between a semi-classical version of this transition and the so-called Manning condensation phenomena in polyelectrolyte physics.

Holographic RG flow triggered by a classically marginal operator

We study the holographic renormalization group (RG) flow triggered by a classically marginal operator. When a marginal operator deforms a conformal field theory, it does not yield a nontrivial renormalization group flow at the classical level. At the quantum level, however, quantum corrections modify a marginal operator into one of the truly marginal, marginally relevant, and marginally irrelevant operators and can generate a nontrivial RG flow. We investigate the holographic description of a RG flow triggered by a marginal operator with quantum corrections. We look into how the physical quantities of a deformed theory, a coupling constant and the vacuum expectation value, rely on the RG scale. We further discuss the holographic description of the trace anomaly caused by the gluon condensation.

Dark Side of Weyl Gravity

We address the issue of a dynamical breakdown of scale invariance in quantum Weyl gravity together with related cosmological implications. In the first part, we build on our previous work [Phys. Rev. D2020, 101, 044050], where we found a non-trivial renormalization group fixed point in the infrared sector of quantum Weyl gravity. Here, we prove that the ensuing non-Gaussian IR fixed point is renormalization scheme independent. This confirms the feasibility of the analog of asymptotic safety scenario for quantum Weyl gravity in the IR. Some features, including non-analyticity and a lack of autonomy, of the system of β-functions near a turning point of the renormalization group at intermediate energies are also described. We further discuss an extension of the renormalization group analysis to the two-loop level. In particular, we show universal properties of the system of β-functions related to three couplings associated with C2 (Weyl square), G (Gauss–Bonnet), and R2 (Ricci curvature square) terms. Finally, we discuss various technical and conceptual issues associated with the conformal (trace) anomaly and propose possible remedies. In the second part, we analyze physics in the broken phase. In particular, we show that, in the low-energy sector of the broken phase, the theory looks like Starobinsky f(R) gravity with a gravi-cosmological constant that has a negative sign in comparison to the usual matter-induced cosmological constant. We discuss implications for cosmic inflation and highlight a non-trivial relation between Starobinsky’s parameter and the gravi-cosmological constant. Salient issues, including possible UV completions of quantum Weyl gravity and the role of the trace anomaly matching, are also discussed.

Effective long distance qoverline{q} potential in holographic RG flows

We study the qoverline{q} potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation L large compared to the characteristic scale of the field theory. These are determined by the leading order IR physics plus a series of corrections, sensitive to the properties of the RG-flow. To determine those corrections, we propose a general method applying holographic Wilsonian renormalization to a dual string. We apply this method to examine in detail two sets of examples, 3 + 1-dimensional theories with an RG flow ending in an IR fixed point; and theories that are confining in the IR, in particular, the Witten QCD and Klebanov-Strassler models. In both cases, we find corrections with a universal dependence on the inter-quark separation. When there is an IR fixed point, that correction decays as a power ∼ 1/L4. We explain that dependence in terms of a double-trace deformation in a one-dimensional defect theory. For a confining theory, the decay is exponential ∼ e−M L, with M a scale of the order of the glueball mass. We interpret this correction using an effective flux tube description as produced by a background internal mode excitation induced by sources localized at the endpoints of the flux tube. We discuss how these results could be confronted with lattice QCD data to test whether the description of confinement via the gauge/gravity is qualitatively correct.

Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity

Here we apply the full Will-Nordtvedt version of the Parameterized Post-Newtonian (PPN) formalism to a class of General Relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant $G$ is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the External Potential Effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales, for any of them the Solar System bounds need to be considered.

Impact of topology in foliated quantum Einstein gravity

We use a functional renormalization group equation tailored to the Arnowitt–Deser–Misner formulation of gravity to study the scale dependence of Newton’s coupling and the cosmological constant on a background spacetime with topology S^1 times S^d. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of “gravitational instability”, modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology S^1 times T^d (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

Holographic trace anomaly at finite temperature

Using the holographic renormalization, we investigate the finite temperature and size effect to the energy-momentum tensor of the dual field theory and its renormalization group (RG) flow. Following the anti-de Sitter/conformal field theory correspondence, the dual field theory of the AdS space is well known to be a conformal field theory that has no nontrivial RG flow. Holographically, that theory can be lifted to a finite temperature version by considering a AdS black hole solution. Because the black hole horizon associated with temperature is dimensionful, it breaks the boundary conformal symmetry and leads to a nontrivial RG flow. In this work, we investigate the finite temperature and size correction to a strongly interacting conformal field theory along the Wisonian renormalization group flow.

Quantum phase transitions in the Belinsky-Khalatnikov-Lifshitz universe

We study quantum corrections to the classical Bianchi I and Bianchi IX universes. The modified dynamics is well-motivated from the asymptotic safety program where the short-distance behavior of gravity is governed by a non-trivial renormalization group fixed point. The correction terms induce a phase transition in the dynamics of the model, changing the classical, chaotic Kasner oscillations into a uniform approach to a point singularity. The resulting implications for the microscopic structure of spacetime are discussed.

Quantum Einstein gravity

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in quantum Einstein gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the causal dynamical triangulation approach.

Entropy Production during Asymptotically Safe Inflation

The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector.

Taming perturbative divergences in asymptotically safe gravity

We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.

Renormalization group and nonequilibrium action in stochastic field theory.

We investigate the renormalization group approach to nonequilibrium field theory. We show that it is possible to derive nontrivial renormalization group flow from iterative coarse graining of a closed-time-path action. This renormalization group is different from the usual in quantum field theory textbooks, in that it describes nontrivial noise and dissipation. We work out a specific example where the variation of the closed-time-path action leads to the so-called Kardar-Parisi-Zhang equation, and show that the renormalization group obtained by coarse graining this action, agrees with the dynamical renormalization group derived by directly coarse graining the equations of motion.

Renormalization group flows for brane couplings

Field theories in the presence of branes encounter localized divergences that renormalize brane couplings. The sources of these brane-localized divergences are understood as arising either from broken translation invariance, or from short distance singularities as the brane thickness vanishes. While the former are generated only by quantum corrections, the latter can appear even at the classical level. Using as an example six-dimensional scalar field theory in the background of a 3-brane, we show how to interpret such classical divergences by the usual regularization and renormalization procedure of quantum field theory. In our example, the zero thickness divergences are logarithmic, and lead classically to non-trivial renormalization group flows for the brane couplings. We construct the tree level renormalization group equations for these couplings as well as the one-loop corrections to these flows from bulk-to-brane renormalization effects.

Supersymmetric domain wall and RG flow from 4-dimensional gauged supergravity

By studying various, known extrema of 1) SU(3) sectors, 2) SO(5) sectors and 3) SO(3)xSO(3) sectors of gauged N =8 supergravity in four-dimensions, one finds that the deformation of seven sphere \S^7 gives rise to non-trivial renormalization group(RG) flow in three-dimensional boundary conformal field theory from UV fixed point to IR fixed point. For SU(3) sectors, this leads to four-parameter subspace of the supergravity scalar-gravity action and we identify one of the eigenvalues of A_1 tensor of the theory with a superpotential of scalar potential that governs RG flows on this subspace. We analyze some of the structure of the superpotential and discuss first-order BPS domain-wall solutions, using some algebraic relations between superpotential and derivatives of it with respect to fields, that determine a (super)symmetric kink solution in four-dimensional N =8 supergravity, which generalizes all the previous considerations. The BPS domain-wall solutions are equivalent to vanishing of variation of spin 1/2, 3/2 fields in the supersymmetry preserving bosonic background of gauged N=8 supergravity. For SO(5) sectors, there exist only nontrivial nonsupersymmetric critical points that are unstable and included in SU(3) sectors. For SO(3)xSO(3) sectors, we construct the scalar potential(never been written) explicitly and study explicit construction of first-order domain-wall solutions.

Three-dimensional SCFTs, supersymmetric domain wall and renormalization group flow

By analyzing SU(3)xU(1) invariant stationary point, studied earlier by Nicolai and Warner, of gauged N=8 supergravity, we find that the deformation of S^7 gives rise to nontrivial renormalization group flow in a three-dimensional boundary super conformal field theory from N=8, SO(8) invariant UV fixed point to N=2, SU(3)xU(1) invariant IR fixed point. By explicitly constructing 28-beins u, v fields, that are an element of fundamental 56-dimensional representation of E_7, in terms of scalar and pseudo-scalar fields of gauged N=8 supergravity, we get A_1, A_2 tensors. Then we identify one of the eigenvalues of A_1 tensor with ``superpotential'' of de Wit-Nicolai scalar potential and discuss four-dimensional supergravity description of renormalization group flow, i.e. the BPS domain wall solutions which are equivalent to vanishing of variation of spin 1/2, 3/2 fields in the supersymmetry preserving bosonic background of gauged N=8 supergravity. A numerical analysis of the steepest descent equations interpolating two critical points is given.

More CFTs and RG flows from deforming M2/M5-brane horizon

Near-horizon geometry of coincident M2-branes at a conical singularity is related to M-theory on AdS 4 times an appropriate seven-dimensional manifold X 7. For X 7= N 0,1,0, squashing deformation is known to lead to spontaneous (super)symmetry breaking from N=(3,0) to N=(0,1) in gauged AdS 4 supergravity. Via AdS/CFT correspondence, it is interpreted as renormalization group flow of strongly coupled three-dimensional field theory with SU(3)× SU(2) global symmetry. The flow interpolates between N=(0,1) fixed point in the UV to N=(3,0) fixed point in the IR. Evidences for the interpretation are found both from critical points of the supergravity scalar potential and from conformal dimension of relevant chiral primary operators at each fixed point. We also analyze cases with X 7= SO(5)/ SO(3) max, V 5,2( R), M 1,1,1, Q 1,1,1 and find that there is no non-trivial renormalization group flows. We extend the analysis to Englert type vacua of M-theory. By analyzing de Wit–Nicolai potential, we find that deformation of S 7 gives rise to renormalization group flow from N=8 , SO(8) invariant UV fixed point to N=1 , G 2 invariant IR fixed point. For AdS 7 supergravity relevant for near-horizon geometry of coincident M5-branes, we also point out a non-trivial renormalization group flow from N=1 superconformal UV fixed point to non-supersymmetric IR fixed point.

Generalized conifolds and four dimensional Script N = 1 superconformal theories

This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The $\mathcal{N}=1$ superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE $\mathcal{N}=2$ superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single $D3$-brane and discuss the near-horizon supergravity solution for a large number $N$ of coincident $D3$-branes.