1,472 research outputs found
A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions
I study various properties of the critical limits of correlators containing
insertions of conserved and anomalous currents. In particular, I show that the
improvement term of the stress tensor can be fixed unambiguously, studying the
RG interpolation between the UV and IR limits. The removal of the improvement
ambiguity is encoded in a variational principle, which makes use of sum rules
for the trace anomalies a and a'. Compatible results follow from the analysis
of the RG equations. I perform a number of self-consistency checks and discuss
the issues in a large set of theories.Comment: 15 page
Renormalization of a class of non-renormalizable theories
Certain power-counting non-renormalizable theories, including the most
general self-interacting scalar fields in four and three dimensions and
fermions in two dimensions, have a simplified renormalization structure. For
example, in four-dimensional scalar theories, 2n derivatives of the fields,
n>1, do not appear before the nth loop. A new kind of expansion can be defined
to treat functions of the fields (but not of their derivatives)
non-perturbatively. I study the conditions under which these theories can be
consistently renormalized with a reduced, eventually finite, set of independent
couplings. I find that in common models the number of couplings sporadically
grows together with the order of the expansion, but the growth is slow and a
reasonably small number of couplings is sufficient to make predictions up to
very high orders. Various examples are solved explicitly at one and two loops.Comment: 38 pages, 1 figure; v2: more explanatory comments and references;
appeared in JHE
Infinite reduction of couplings in non-renormalizable quantum field theory
I study the problem of renormalizing a non-renormalizable theory with a
reduced, eventually finite, set of independent couplings. The idea is to look
for special relations that express the coefficients of the irrelevant terms as
unique functions of a reduced set of independent couplings lambda, such that
the divergences are removed by means of field redefinitions plus
renormalization constants for the lambda's. I consider non-renormalizable
theories whose renormalizable subsector R is interacting and does not contain
relevant parameters. The "infinite" reduction is determined by i) perturbative
meromorphy around the free-field limit of R, or ii) analyticity around the
interacting fixed point of R. In general, prescriptions i) and ii) mutually
exclude each other. When the reduction is formulated using i), the number of
independent couplings remains finite or slowly grows together with the order of
the expansion. The growth is slow in the sense that a reasonably small set of
parameters is sufficient to make predictions up to very high orders. Instead,
in case ii) the number of couplings generically remains finite. The infinite
reduction is a tool to classify the irrelevant interactions and address the
problem of their physical selection.Comment: 40 pages; v2: more explanatory comments; appeared in JHE
Higher-spin current multiplets in operator-product expansions
Various formulas for currents with arbitrary spin are worked out in general
space-time dimension, in the free field limit and, at the bare level, in
presence of interactions. As the n-dimensional generalization of the
(conformal) vector field, the (n/2-1)-form is used. The two-point functions and
the higher-spin central charges are evaluated at one loop. As an application,
the higher-spin hierarchies generated by the stress-tensor operator-product
expansion are computed in supersymmetric theories. The results exhibit an
interesting universality.Comment: 19 pages. Introductory paragraph, misprint corrected and updated
references. CQG in pres
Consistent irrelevant deformations of interacting conformal field theories
I show that under certain conditions it is possible to define consistent
irrelevant deformations of interacting conformal field theories. The
deformations are finite or have a unique running scale ("quasi-finite"). They
are made of an infinite number of lagrangian terms and a finite number of
independent parameters that renormalize coherently. The coefficients of the
irrelevant terms are determined imposing that the beta functions of the
dimensionless combinations of couplings vanish ("quasi-finiteness equations").
The expansion in powers of the energy is meaningful for energies much smaller
than an effective Planck mass. Multiple deformations can be considered also. I
study the general conditions to have non-trivial solutions. As an example, I
construct the Pauli deformation of the IR fixed point of massless non-Abelian
Yang-Mills theory with N_c colors and N_f <~ 11N_c/2 flavors and compute the
couplings of the term F^3 and the four-fermion vertices. Another interesting
application is the construction of finite chiral irrelevant deformations of N=2
and N=4 superconformal field theories. The results of this paper suggest that
power-counting non-renormalizable theories might play a role in the description
of fundamental physics.Comment: 23 pages, 5 figures; reference updated - JHE
Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility
I discuss several issues about the irreversibility of the RG flow and the
trace anomalies c, a and a'. First I argue that in quantum field theory: i) the
scheme-invariant area Delta(a') of the graph of the effective beta function
between the fixed points defines the length of the RG flow; ii) the minimum of
Delta(a') in the space of flows connecting the same UV and IR fixed points
defines the (oriented) distance between the fixed points; iii) in even
dimensions, the distance between the fixed points is equal to
Delta(a)=a_UV-a_IR. In even dimensions, these statements imply the inequalities
0 =< Delta(a)=< Delta(a') and therefore the irreversibility of the RG flow.
Another consequence is the inequality a =< c for free scalars and fermions (but
not vectors), which can be checked explicitly. Secondly, I elaborate a more
general axiomatic set-up where irreversibility is defined as the statement that
there exist no pairs of non-trivial flows connecting interchanged UV and IR
fixed points. The axioms, based on the notions of length of the flow, oriented
distance between the fixed points and certain "oriented-triangle inequalities",
imply the irreversibility of the RG flow without a global a function. I
conjecture that the RG flow is irreversible also in odd dimensions (without a
global a function). In support of this, I check the axioms of irreversibility
in a class of d=3 theories where the RG flow is integrable at each order of the
large N expansion.Comment: 24 pages, 3 figures; expanded intro, improved presentation,
references added - CQ
Low-energy Phenomenology Of Scalarless Standard-Model Extensions With High-Energy Lorentz Violation
We consider renormalizable Standard-Model extensions that violate Lorentz
symmetry at high energies, but preserve CPT, and do not contain elementary
scalar fields. A Nambu--Jona-Lasinio mechanism gives masses to fermions and
gauge bosons, and generates composite Higgs fields at low energies. We study
the effective potential at the leading order of the large-N_{c} expansion,
prove that there exists a broken phase and study the phase space. In general,
the minimum may break invariance under boosts, rotations and CPT, but we give
evidence that there exists a Lorentz invariant phase. We study the spectrum of
composite bosons and the low-energy theory in the Lorentz phase. Our approach
predicts relations among the parameters of the low-energy theory. We find that
such relations are compatible with the experimental data, within theoretical
errors. We also study the mixing among generations, the emergence of the CKM
matrix and neutrino oscillations.Comment: 32 pages; v2: typos corrected, more references, some more comments -
PR
Tailoring Dielectric Properties of Multilayer Composites Using Spark Plasma Sintering
A straightforward and simple way to produce well-densified ferroelectric ceramic composites with a full control of both architecture and properties using spark plasma sintering (SPS) is proposed. SPS main outcome is indeed to obtain high densification at relatively low temperatures and short treatment times thus limiting interdiffusion in multimaterials. Ferroelectric/dielectric (BST64/MgO/BST64) multilayer ceramic densified at 97% was obtained, with unmodified Curie temperature, a stack dielectric constant reaching 600, and dielectric losses dropping down to 0.5%, at room-temperature. This result ascertains SPS as a relevant tool for the design of functional materials with tailored properties
Holomorphic Currents and Duality in N=1 Supersymmetric Theories
Twisted supersymmetric theories on a product of two Riemann surfaces possess
non-local holomorphic currents in a BRST cohomology. The holomorphic currents
act as vector fields on the chiral ring. The OPE's of these currents are
invariant under the renormalization group flow up to BRST-exact terms. In the
context of electric-magnetic duality, the algebra generated by the holomorphic
currents in the electric theory is isomorphic to the one on the magnetic side.
For the currents corresponding to global symmetries this isomorphism follows
from 't Hooft anomaly matching conditions. The isomorphism between OPE's of the
currents corresponding to non-linear transformations of fields of matter
imposes non-trivial conditions on the duality map of chiral ring. We consider
in detail the SQCD with matter in fundamental and adjoint
representations, and find agreement with the duality map proposed by Kutasov,
Schwimmer and Seiberg.Comment: 19 pages, JHEP3 LaTex, typos correcte
Lorentz violating kinematics: Threshold theorems
Recent tentative experimental indications, and the subsequent theoretical
speculations, regarding possible violations of Lorentz invariance have
attracted a vast amount of attention. An important technical issue that
considerably complicates detailed calculations in any such scenario, is that
once one violates Lorentz invariance the analysis of thresholds in both
scattering and decay processes becomes extremely subtle, with many new and
naively unexpected effects. In the current article we develop several extremely
general threshold theorems that depend only on the existence of some energy
momentum relation E(p), eschewing even assumptions of isotropy or monotonicity.
We shall argue that there are physically interesting situations where such a
level of generality is called for, and that existing (partial) results in the
literature make unnecessary technical assumptions. Even in this most general of
settings, we show that at threshold all final state particles move with the
same 3-velocity, while initial state particles must have 3-velocities
parallel/anti-parallel to the final state particles. In contrast the various
3-momenta can behave in a complicated and counter-intuitive manner.Comment: V1: 32 pages, 6 figures, 3 tables. V2: 5 references adde
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