<p>We investigate a class of quantum field theories with relativistic Luttinger fermions and local self-interaction in scalar channels. For an understanding of possible low-energy phases, we first classify the set of mass terms arising from scalar fermion bilinears. For large flavor numbers, we show that each of our models features a coupling branch in which the theory is asymptotically free. In order to address the long-range behavior, we use mean-field theory which is exact in the limit of large flavor numbers. We identify two models which undergo dimensional transmutation, interconnecting the asymptotically free high-energy regime with an ordered low-energy phase sustaining a vacuum condensate. We also study the analytic structure of the Luttinger-fermionic propagator in the various possible gapped phases.</p>

Germany

Holger Gies

Marta Picciau

Mean-field theory for self-interacting relativistic Luttinger fermions

<p>Laser pulse collisions are a promising tool for the investigation of light-by-light scattering phenomena induced by quantum vacuum fluctuations. Using the numerical code based on the vacuum emission picture and put forward in [1], we observe a strong dependence of the signal features on the transverse profiles of the colliding laser pulses in the interaction region. For a probe beam tailored such as to feature an annular far-field profile and a pronounced on-axis focus peak counterpropagating a pump beam at zero impact parameter, the signal’s main emission direction can undergo the analog of a phase transition with the beam-waist ratio of the pulses serving as a control parameter. Depending on the pump’s beam profile, this phase transition can be first order (e.g., for a pump with a flat-top far-field profile) or second order (e.g., for a Gaussian pump). From the simulation data, we determine the critical point and extract the corresponding critical exponent for the second-order transition of the main emission direction of the signal in the far field. For this, we improve the performance of the above numerical code, using the phase transition analogs as an example to illustrate the capabilities and limitations of the code and current workflows.</p>

Felix Karbstein

Lars Maiwald

Phase transition analogs in laser collisions with a dark-field setup

We investigate nonperturbative aspects of the interplay of chiral transitions in the standard model in the course of the renormalization flow. We focus on the chiral symmetry breaking mechanisms provided by the QCD and the electroweak sectors, the latter of which we model by a Higgs-top-bottom Yukawa theory. The interplay becomes quantitatively accessible by accounting for the fluctuation-induced mixing of the electroweak Higgs field with the mesonic composite fields of QCD. In fact, our approach uses dynamical bosonization and treats these scalar fields on the same footing. Varying the QCD scale relative to the Fermi scale we quantify the mutual impact of the symmetry-breaking mechanisms, specifically the departure from the second order quantum phase transition of the pure Yukawa sector in favor of a crossover upon the inclusion of the gauge interactions. This allows to discuss the “naturalness” of the standard model in terms of a pseudo-critical exponent which we determine as a function of the ratio of the QCD and the Fermi scale. We also estimate the minimum value of the boson mass in absence of the Higgs mechanism.

Richard Schmieden

Italy

Luca Zambelli

Interplay of chiral transitions in the standard model

We study the renormalization flow of generic actions that depend on the invariants of the field strength tensor of an Abelian gauge field. While the Maxwell action defines a Gaussian fixed point, we search for further non-Gaussian fixed points or rather fixed functions, i.e., globally existing Lagrangians of the invariants. Using standard small-field expansion techniques for the resulting functional flow equation, a large number of fixed points is obtained, which—in analogy to recent findings for a shift-symmetric scalar field—we consider as approximation artifacts. For the construction of a globally existing fixed function, we pay attention to the use of proper initial conditions. Parametrizing the latter by the photon anomalous dimension, both the coefficients of the weak-field expansion are fully determined and those of the large-field expansion can be matched such that a global fixed function can be constructed for magnetic fields. The anomalous dimension also governs the strong-field limit. Our results provide evidence for the existence of a continuum of non-Gaussian fixed points parametrized by a small positive anomalous dimension below a critical value. We discuss the implications of this result within various scenarios with and without additional matter. For the strong-field limit of the 1PI QED effective action, where the anomalous dimension is determined by electronic fluctuations, our result suggests the existence of a singularity free strong-field limit, circumventing the standard conclusions connected to the perturbative Landau pole.

Julian Schirrmeister

Renormalization flow of nonlinear electrodynamics

We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using the spin-base invariant formalism. The corresponding minimal spinor has 32 complex components, matching with the degrees of freedom of a standard-model generation including a right-handed neutrino. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories. In particular, new asymptotically free self-interacting field theories can be constructed, representing first examples of high-energy complete quantum field theories based on pure matter degrees of freedom. Gauge theories with relativistic Luttinger fermions exhibit a strong paramagnetic dominance, requiring large non-Abelian gauge groups to maintain asymptotic freedom. We comment on the possibility to use Luttinger fermions for particle physics model building and the expected naturalness properties of such models.

Philip Heinzel

Johannes Laufkötter

Quantum field theories of relativistic Luttinger fermions

We test the physical viability of a recent proposal for an asymptotically safe modification of quantum electrodynamics (QED), whose ultraviolet physics is dominated by a non-perturbative Pauli spin-field coupling. We focus in particular on its compatibility with the absence of dynamical generation of fermion mass in QED. Studying the renormalization group flow of chiral four-fermion operators and their fixed points, we discover a distinct class of behavior compared to the standard picture of fixed-point annihilation at large gauge couplings and the ensuing formation of chiral condensates. Instead, transcritical bifurcations, where the fixed points merely exchange infrared stability, are observed. Provided that non-chiral operators remain irrelevant, our theory accommodates a universality class of light fermions for  $$N_{\textrm{f}}&gt; 1$$  <math> <mrow> <msub> <mi>N</mi> <mtext>f</mtext> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </math>   irreducible Dirac flavors. On the contrary, in the special case of  $$N_{\textrm{f}}= 1$$  <math> <mrow> <msub> <mi>N</mi> <mtext>f</mtext> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math>   flavor, this comes only at the expense of introducing one additional relevant parameter.

Kevin Tam

Fermionic fixed-point structure of asymptotically safe QED with a Pauli term

We explore the fixed-point structure of QED-like theories upon the inclusion of a Pauli spin-field coupling. We concentrate on the fate of UV-stable fixed points recently discovered in  $$d=4$$  <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>4</mn> </mrow> </math>   spacetime dimensions upon generalizations to lower as well as higher dimensions for an arbitrary number of fermion flavors  $$N_{\text {f}}.$$  <math> <mrow> <msub> <mi>N</mi> <mtext>f</mtext> </msub> <mo>.</mo> </mrow> </math>   As an overall trend, we observe that going away from  $$d=4$$  <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>4</mn> </mrow> </math>   dimensions and increasing the flavor number tends to destabilize the non-Gaussian fixed points discovered in four spacetime dimensions. A notable exception is a non-Gaussian fixed point at finite Pauli spin-field coupling but vanishing gauge coupling, which also remains stable down to  $$d=3$$  <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>3</mn> </mrow> </math>   dimensions and for small flavor numbers. This includes also the range of degrees of freedom used in effective theories of layered condensed-matter systems. As an application, we construct renormalization group trajectories that emanate from the non-Gaussian fixed point and approach a long-range regime in the conventional QED $${}_3$$  <math> <msub> <mrow></mrow> <mn>3</mn> </msub> </math>   universality class that is governed by the interacting (quasi) fixed point in the gauge coupling.

Jobst Ziebell

Pauli-term-induced fixed points in d-dimensional QED

We study the renormalization flow of Hilbert–Palatini gravity to lowest non-trivial order. We find evidence for an asymptotically safe high-energy completion based on the existence of an ultraviolet fixed point similar to the Reuter fixed point of quantum Einstein gravity. In order to manage the quantization of the large number of independent degrees of freedom in terms of the metric as well as the connection, we use an on-shell reduction scheme: for this, we quantize all degrees of freedom beyond Einstein gravity at a given order that remain after using the equations of motion at the preceding order. In this way, we can straightforwardly keep track of the differences emerging from quantizing Hilbert–Palatini gravity in comparison with Einstein gravity. To lowest non-trivial order, the difference is parametrized by fluctuations of an additional abelian gauge field. The critical properties of the ultraviolet fixed point of Hilbert–Palatini gravity are similar to those of the Reuter fixed point, occurring at a smaller Newton coupling and exhibiting more stable higher order exponents.

Abdol Salek

Asymptotically safe Hilbert–Palatini gravity in an on-shell reduction scheme

We combine a recent construction of a Becchi-Rouet-Stora-Tyutin (BRST)-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background-field invariance as well as BRST invariance of the quantum field manifestly. The construction features BRST-invariant mass parameters for the quantum gauge and ghost fields. The formalism employs a background Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and thus should not affect observables. We verify this expectation by computing the one-loop effective action and the beta function of the gauge coupling as an example. The corresponding Schwinger functional generating connected correlation functions acquires additional one-particle reducible terms that vanish on shell. We also study off-shell one-loop contributions in order to explore the consequences of a nonlinear gauge fixing scheme involving a background Nakanishi-Lautrup field. As an application, we show that our formalism straightforwardly accommodates nonperturbative information about propagators in the Landau gauge in the form of the so-called decoupling solution. Using this nonperturbative input, we find evidence for the formation of a gluon condensate for sufficiently large coupling, whose scale is set by the BRST-invariant gluon mass parameter.

Dimitrios Gkiatas

Background effective action with nonlinear massive gauge fixing

We study the collision of two optical laser pulses in a pump-probe setup using beams with circular and elliptic cross section and estimate the number of discernible signal photons induced by quantum vacuum nonlinearities. In this analysis we study strategies to optimize the quantum vacuum signal discernible from the background of the driving lasers. One of the main results is that the collision of two maximally focused lasers does not lead to the best discernible signal. Instead, widening the focus typically improves the signal to background separation in the far field. For petawatt class lasers, an optimal choice of the focus waist yields several discernible photons per shot in contrast to no discernible signal for tight focusing. Further enhancement is possible by using an elliptical waist.