909 research outputs found
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
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
HyperK\"ahler quotients and N=4 gauge theories in D=2
We consider certain N=4 supersymmetric gauge theories in D=2 coupled to
quaternionic matter multiplets in a minimal way. These theories admit as
effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained
as HyperK\"ahler quotients. The example of ALE manifolds is discussed. (Based
on a talk given by P. Fr\'e at the F. Gursey Memorial Conference, Istanbul,
June 1994).Comment: 22 pages, Latex, no figure
The Linear Point: A cleaner cosmological standard ruler
We show how a characteristic length scale imprinted in the galaxy two-point
correlation function, dubbed the "linear point", can serve as a comoving
cosmological standard ruler. In contrast to the Baryon Acoustic Oscillation
peak location, this scale is constant in redshift and is unaffected by
non-linear effects to within percent precision. We measure the location
of the linear point in the galaxy correlation function of the LOWZ and CMASS
samples from the Twelfth Data Release (DR12) of the Baryon Oscillation
Spectroscopic Survey (BOSS) collaboration. We combine our linear-point
measurement with cosmic-microwave-background constraints from the Planck
satellite to estimate the isotropic-volume distance , without relying
on a model-template or reconstruction method. We find
Mpc and Mpc respectively, consistent with the quoted
values from the BOSS collaboration. This remarkable result suggests that all
the distance information contained in the baryon acoustic oscillations can be
conveniently compressed into the single length associated with the linear
point.Comment: The optimal two-point correlation function bin-size is employed.
Results are updated and the distance constraints are improve
On field theory quantization around instantons
With the perspective of looking for experimentally detectable physical
applications of the so-called topological embedding, a procedure recently
proposed by the author for quantizing a field theory around a non-discrete
space of classical minima (instantons, for example), the physical implications
are discussed in a ``theoretical'' framework, the ideas are collected in a
simple logical scheme and the topological version of the Ginzburg-Landau theory
of superconductivity is solved in the intermediate situation between type I and
type II superconductors.Comment: 27 pages, 5 figures, LaTe
Structure of the Electric Flux in N=4 Supersymmetric Yang-Mills Theory
Correlators of Wilson loop operators with O_4=Tr(F_{\mu\nu}^2+...) are
computed in N=4 super-Yang-Mills theory using the AdS/CFT correspondence. The
results are compared with the leading order perturbative computations. As a
consequence of conformal invariance, these correlators have identical forms in
the weak and strong coupling limits for circular loops. They are essentially
different for contours not protected by conformal symmetry.Comment: 7 pages, 1 postscript figure, minor corrections and clarifying
argument
A three-loop check of the 'a - maximization' in SQCD with adjoint(s)
The 'a - maximization' was introduced by K. Inrtiligator and B. Wecht for
finding anomalous dimensions of chiral superfields at the IR fixed points of
the RG flow. Using known explicit calculations of anomalous dimensions in the
perturbation theory of SQCD (with one or two additional adjoint fields), it is
checked here at the three-loop level.Comment: 5 pages; the title changed, the text improved and expande
Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
Superselection rules (SSRs) limit the mechanical and quantum processing
resources represented by quantum states. However SSRs can be violated using
reference systems to break the underlying symmetry. We show that there is a
duality between the ability of a system to do mechanical work and to act as a
reference system. Further, for a bipartite system in a globally symmetric pure
state, we find a triality between the system's ability to do local mechanical
work, its ability to do ``logical work'' due to its accessible entanglement,
and its ability to act as a shared reference system.Comment: 5 pages, no figures. Extended resubmitted version. Slightly modified
title. Transferred to PR
Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories
We consider the one-loop effective potential at zero and finite temperature
in field theories with anisotropic space-time scaling, with critical exponent
, including both scalar and gauge fields. Depending on the relative
strength of the coupling constants for the gauge and scalar interactions, we
find that there is a symmetry breaking term induced at one-loop at zero
temperature and we find symmetry restoration through a first-order phase
transition at high temperature.Comment: 12 pages, 2 figures, final version accepted in Phys. Let
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