220 research outputs found
Status of twist-2 operator dimensions at O(1/N_f)
We review the computation of the anomalous dimensions of the twist-2
unpolarized operators in the large N_f expansion. Results are discussed for the
predominantly gluonic singlet operator and the O(1/N_f) part of the 3-loop
splitting function is given.Comment: 4 latex pages, contribution to DIS 9
Critical exponent omega in the Gross-Neveu-Yukawa model at O(1/N)
The critcal exponent is evaluated at in -dimensions in
the Gross-Neveu model using the large critical point formalism. It is shown
to be in agreement with the recently determined three loop -functions of
the Gross-Neveu-Yukawa model in four dimensions. The same exponent is computed
for the chiral Gross-Neveu and non-abelian Nambu-Jona-Lasinio universality
classes.Comment: 16 latex pages, 5 figures, typos corrected and text adde
Eight dimensional QCD at one loop
The Lagrangian for a non-abelian gauge theory with an symmetry
and a linear covariant gauge fixing is constructed in eight dimensions. The
renormalization group functions are computed at one loop with the special cases
of and treated separately. By computing the critical
exponents derived from these in the large expansion at the
Wilson-Fisher fixed point it is shown that the Lagrangian is in the same
universality class as the two dimensional non-abelian Thirring model and
Quantum Chromodynamics (QCD). As the eight dimensional Lagrangian contains new
quartic gluon operators not present in four dimensional QCD, we compute in
parallel the mixing matrix of four dimensional dimension operators in pure
Yang-Mills theory.Comment: 31 latex pages, anc directory now added which contains txt file of
all renormalization group function
beta-functions in higher dimensional field theories
We review recent activity in the construction of the renormalization group functions for O(N) scalar and gauge theories in six and higher dimensions. The theories lie in their respective universality classes at the Wilson-Fisher fixed point. The critical exponents at this fixed point in the various dimensions are all in agreement with the known exponents determined in the large Nexpansion
Asymptotic freedom from the two-loop term of the beta function in a cubic theory
We renormalize a six dimensional cubic theory to four loops in the MSbar
scheme where the scalar is in a bi-adjoint representation. The underlying model
was originally derived in a problem relating to gravity being a double copy of
Yang-Mills theory. As a field theory in its own right we find that it has a
curious property in that while unexpectedly there is no one loop contribution
to the -function the two loop coefficient is negative. It therefore
represents an example where asymptotic freedom is determined by the two loop
term of the -function. We also examine a multi-adjoint cubic theory in
order to see whether this is a more universal property of these models.Comment: 17 latex page
Vertex functions in QCD - preparation for beyond two loops
We summarize the algorithm to determine the two loop off-shell 3-point vertexfunctions of QCD before outlining the steps required to extend the results tothree and higher loops
Quark mass anomalous dimension at O(1/N_f^2) in QCD
We compute the d-dimensional critical exponents corresponding to the wave
function and mass renormalization of the quark in QCD in the Landau gauge at a
new order, O(1/N_f^2), in the large N_f expansion. The computations are
simplified by the establishment in d-dimensions of the critical point
equivalence of QCD and the non-abelian Thirring model beyond leading order. The
form of the O(1/N_f^2) coefficients in the MSbar quark mass anomalous dimension
at five loops is deduced and compared with the numerical asymptotic Pade
approximant prediction.Comment: 13 latex pages, 3 eps figure
Higher dimensional higher derivative φ⁴ theory
We construct several towers of scalar quantum field theories with an
symmetry which have higher derivative kinetic terms. The Lagrangians in each
tower are connected by lying in the same universality class at the
-dimensional Wilson-Fisher fixed point. Moreover the universal theory is
studied using the large expansion and we determine -dimensional critical
exponents to . We show that these new universality classes emerge
naturally as solutions to the linear relation of the dimensions of the fields
deduced from the underlying force-matter interaction of the universal critical
theory. To substantiate the equivalence of the Lagrangians in each tower we
renormalize each to several loop orders and show that the renormalization group
functions are consistent with the large critical exponents. While we focus
on the first two new towers of theories and renormalize the respective
Lagrangians to and dimensions there are an infinite number of such
towers. We also briefly discuss the conformal windows and the extension of the
ideas to theories with spin- and spin- fields as well as the
idea of lower dimension completeness.Comment: 30 latex pages, minor typos correcte
Three loop effective potential for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">⟨</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:msup><mml:mrow><mml:msubsup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">⟩</mml:mo></mml:mrow></mml:math> in the Landau gauge in QCD
We apply the Local Composite Operator method to construct the three loop
effective potential for the dimension two operator
in the Landau gauge in Quantum Chromodynamics. For we show that the
three loop value of the effective mass of the gluon is similar to the two loop
estimates when the number of massless quarks is strictly less than five for
.Comment: 29 latex pages, 5 figures, 11 tables, minor text change
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