11 research outputs found
Critical behavior of Dirac fermions from perturbative renormalization
Gapless Dirac fermions appear as quasiparticle excitations in various
condensed-matter systems. They feature quantum critical points with critical
behavior in the 2+1 dimensional Gross-Neveu universality class. The precise
determination of their critical exponents defines a prime benchmark for
complementary theoretical approaches, such as lattice simulations, the
renormalization group and the conformal bootstrap. Despite promising recent
developments in each of these methods, however, no satisfactory consensus on
the fermionic critical exponents has been achieved, so far. Here, we perform a
comprehensive analysis of the Ising Gross-Neveu universality classes based on
the recently achieved four-loop perturbative calculations. We combine the
perturbative series in spacetime dimensions with the one for the
purely fermionic Gross-Neveu model in dimensions by employing
polynomial interpolation as well as two-sided Pad\'e approximants. Further, we
provide predictions for the critical exponents exploring various resummation
techniques following the strategies developed for the three-dimensional scalar
universality classes. We give an exhaustive appraisal of the current
situation of Gross-Neveu universality by comparison to other methods. For large
enough number of spinor components as well as for the case of
emergent supersymmetry , we find our renormalization group estimates to be
in excellent agreement with the conformal bootstrap, building a strong case for
the validity of these values. For intermediate as well as in comparison
with recent Monte Carlo results, deviations are found and critically discussed.Comment: 21 pages, 7 figures, 6 table
Deconfined criticality from the QED-Gross-Neveu model at three loops
The QED-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory
involving Dirac fermions and a critical real scalar field. This theory has
recently been argued to represent a dual description of the deconfined quantum
critical point between Neel and valence bond solid orders in frustrated quantum
magnets. We study the critical behavior of the QED-Gross-Neveu model by
means of an epsilon expansion around the upper critical space-time dimension of
up to the three-loop order. Estimates for critical exponents in 2+1
dimensions are obtained by evaluating the different Pade approximants of their
series expansion in epsilon. We find that these estimates, within the spread of
the Pade approximants, satisfy a nontrivial scaling relation which follows from
the emergent SO(5) symmetry implied by the duality conjecture. We also
construct explicit evidence for the equivalence between the QED-Gross-Neveu
model and a corresponding critical four-fermion gauge theory that was
previously studied within the 1/N expansion in space-time dimensions 2<D<4.Comment: 16 pages, 4 figures, 4 tables; v2: additional comments, published
versio
Gauge Coupling Beta Functions in the Standard Model to Three Loops
In this paper we compute the three-loop corrections to the beta functions of
the three gauge couplings in the Standard Model of particle physics using the
minimal subtraction scheme and taking into account Yukawa and Higgs self
couplings.Comment: 4 pages, 1 figure, v2: minor changes, references adde
The four-loop DRED gauge beta-function and fermion mass anomalous dimension for general gauge groups
We present four-loop results for the gauge beta-function and the fermion mass
anomalous dimension for a gauge theory with a general gauge group and a
multiplet of fermions transforming according to an arbitrary representation,
calculated using the dimensional reduction scheme. In the special case of a
supersymmetric theory we confirm previous calculations of both the gauge
beta-function and the gaugino mass beta-function.Comment: 44 pages, added references (v2) minor changes (v3
Renormalization constants and beta functions for the gauge couplings of the Standard Model to three-loop order
We compute the beta functions for the three gauge couplings of the Standard
Model in the minimal subtraction scheme to three loops. We take into account
contributions from all sectors of the Standard Model. The calculation is
performed using both Lorenz gauge in the unbroken phase of the Standard Model
and background field gauge in the spontaneously broken phase. Furthermore, we
describe in detail the treatment of and present the automated setup
which we use for the calculation of the Feynman diagrams. It starts with the
generation of the Feynman rules and leads to the bare result for the Green's
function of a given process.Comment: 44 pages, 9 figures; v2: sign in eq.(29) corrected; final result
unchange
Four-loop beta function and mass anomalous dimension in Dimensional Reduction
Within the framework of QCD we compute renormalization constants for the
strong coupling and the quark masses to four-loop order. We apply the DR-bar
scheme and put special emphasis on the additional couplings which have to be
taken into account. This concerns the epsilon-scalar--quark Yukawa coupling as
well as the vertex containing four epsilon-scalars. For a supersymmetric Yang
Mills theory, we find, in contrast to a previous claim, that the evanescent
Yukawa coupling equals the strong coupling constant through three loops as
required by supersymmetry.Comment: 15 pages, fixed typo in Eq. (18
Four-loop critical exponents for the Gross-Neveu-Yukawa models
We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4 - epsilon dimensions and compute critical exponents for the GrossNeveu- Yukawa fixed points to order O(epsilon(4)). Further, we provide Pade estimates for the correlation length exponent, the boson and fermion anomalous dimension, as well as the leading correction to scaling exponent in 2 + 1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N = 1/4 and N = 1/2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators
Four-loop critical exponents for the Gross-Neveu-Yukawa models
We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4−ε dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order O(ε). Further, we provide Padé estimates for the correlation length exponent, the boson and fermion anomalous dimension, as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N = 1/4 and N = 1/2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators