We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories and extend the results to semisimple groups. In this regime these theories develop an interacting ultraviolet fixed point that for the semisimple case leads to a rich phase diagram. The latter contains a complete asymptotically safe fixed point repulsive in all couplings. We then add two gauged Weyl fermions belonging to arbitrary representations of the semisimple gauge group and a complex, gauged scalar to the original gauge-fermion theory allowing for new Yukawa interactions and quartic scalar self-coupling. Consequently, we determine the first nontrivial order in 1=N f for the Yukawa and quartic beta functions. Our work elucidates, consolidates, and extends results obtained earlier in the literature. We also acquire relevant knowledge about the dynamics of gauge-Yukawa theories beyond perturbation theory. Our findings are applicable to any extension of the standard model featuring a large number of fermions such as asymptotic safety.

We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the non-perturbative corrections and to extend the validity of the eft to any value of the charge. We conjecture the general form of the non-perturbative behavior of the conformal dimensions for any value of N and find very good agreement with previous lattice data.

We study the thermodynamic history of composite dark matter models. We start with classifying the models by means of the symmetries partially protecting the composite dark matter decays and constrain their lifetimes. For each model, we determine the impact of number-changing and number-conserving operators on its thermal history. We also develop the analytic formalism to calculate the asymptotic abundance of stable relics. We show how the relative strength between number-changing and numberconserving interactions together with the dark plasma lifetime affect the thermal fate of the various composite models. Additionally, we show that the final dark relic density of composite particles can be diluted due to an entropy increase stemming from dark plasma decay. Finally, we confront the models with experimental bounds. We find that indirect detection experiments are most promising in testing this large class of models.

We propose a self-consistency equation for the β-function for theories with a large number of flavours, N , that exploits all the available information in the Wilson-Fisher critical exponent, ω, truncated at a fixed order in 1/N . We show that singularities appearing in critical exponents do not necessarily imply singularities in the β-function. We apply our method to (non-)abelian gauge theory, where ω features a negative singularity. The singularities in the β-function and in the fermion mass anomalous dimension are simultaneously removed providing no hint for a UV fixed point in the large-N limit.Introduction.-There are indications that perturbative series in quantum field theory are, in general, asymptotic series with zero radius of convergence. In theories with a large number of flavour-like degrees of freedom, N , a re-organization of the perturbative expansion in powers of 1/N is convenient. It can be shown that at fixed order in 1/N expansion, the number of diagrams contributing grows only polynomially rather than factorially: convergent series are obtained that can be summed up within their radius of convergence.There is a vast literature on resummed results corresponding to the first few orders in 1/N expansion, mainly for RG functions obtained via direct diagram resummation or critical-point methods, see e.g. Refs .Since the perturbative series at fixed order in 1/N are convergent, singularities in the (generically complex) coupling are expected. Appearance of such singularities on the real-coupling axis seems to be true for all the d = 4 theories analyzed so far, thereby having a dramatic effect on RG flows. In particular, the appearance of singularities in the coefficients of the 1/N expansion for gauge and Yukawa β-functions have inspired speculations of a possible UV fixed point [23][24][25][26][27][28][29].More generally, the UV fate of gauge theories for which asymptotic freedom is lost has broad theoretical interest, and this is in fact the case of matter-dominated theories. There, a non-trivial zero of the β-function can be envisaged if the large-N resummation produces a contribution to β functions such that lim g→r β 1/N (g) = −∞, where r is the radius of convergence of the 1/N series. Near the singularity, the O(1/N ) contribution exceeds the leading-order result, and it is clear that a zero must emerge. Unfortunately, close to the radius of convergence the perturbative expansion in 1/N is broken, and higher-order cannot be neglected. Further shadow on the existence of the fixed point as a consistent conformal field theory is cast by studying anomalous dimensions of other operators in the vicinity of the β-function singularity: in the case of large-N QED truncated at O(1/N ), the anomalous dimension of the fermion mass diverges [1, 2], and it was recently pointed out that in the large-N QCD the anomalous dimension of the glueball operator breaks the unitarity bound [30]. Recently, the first lattice simulations to investigate the existence of possible fixed points appeared [31]. Even though th...

A framework for UV completing particle theories is proposed, based on the worldline formalism, which is equivalent to weighting all sums over histories with a proper-time dependent measure that has a smallest proper-time. We deduce a criterion to avoid ghosts, and find that the ghost-free theories have the (string-theory inspired) infinite-derivative model of Siegel as a special case, but represent a significant generalisation. Generically, the UV of such theories is dominated by a saddle-point in the proper-time, leading to simplification in the computation of amplitudes. We focus on a particularly attractive option which is to mimic the regulating properties of modular invariance with a worldline "inversion symmetry".