350 research outputs found
Renormalization of gauge invariant composite operators in light-cone gauge
We generalize to composite operators concepts and techniques which have been
successful in proving renormalization of the effective Action in light-cone
gauge. Gauge invariant operators can be grouped into classes, closed under
renormalization, which is matrix-wise. In spite of the presence of non-local
counterterms, an ``effective" dimensional hierarchy still guarantees that any
class is endowed with a finite number of elements. The main result we find is
that gauge invariant operators under renormalization mix only among themselves,
thanks to the very simple structure of Lee-Ward identities in this gauge,
contrary to their behaviour in covariant gauges.Comment: 35100 Padova, Italy DFPD 93/TH/53, July 1993
documentstyle[preprint,aps]{revtex
Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription
We find the exact non-perturbative expression for a simple Wilson loop of
arbitrary shape for U(N) and SU(N) Euclidean or Minkowskian two-dimensional
Yang-Mills theory regulated by the Wu-Mandelstam-Leibbrandt gauge prescription.
The result differs from the standard pure exponential area-law of YM_2, but
still exhibits confinement as well as invariance under area-preserving
diffeomorphisms and generalized axial gauge transformations. We show that the
large N limit is NOT a good approximation to the model at finite N and conclude
that Wu's N=infinity Bethe-Salpeter equation for QCD_2 should have no bound
state solutions. The main significance of our results derives from the
importance of the Wu-Mandelstam-Leibbrandt prescription in higher-dimensional
perturbative gauge theory.Comment: 7 pages, LaTeX, REVTE
Light--like Wilson loops and gauge invariance of Yang--Mills theory in 1+1 dimensions
A light-like Wilson loop is computed in perturbation theory up to for pure Yang--Mills theory in 1+1 dimensions, using Feynman and
light--cone gauges to check its gauge invariance. After dimensional
regularization in intermediate steps, a finite gauge invariant result is
obtained, which however does not exhibit abelian exponentiation. Our result is
at variance with the common belief that pure Yang--Mills theory is free in 1+1
dimensions, apart perhaps from topological effects.Comment: 10 pages, plain TeX, DFPD 94/TH/
Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
We study correlation functions of Wilson loops and local operators in a
subsector of N=4 SYM which preserves two supercharges. Localization arguments
allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills
theory. In turn, this can be reduced to computing correlators in certain
Gaussian multi-matrix models. We focus on the correlation function of a Wilson
loop and two local operators, and solve the corresponding three-matrix model
exactly in the planar limit. We compare the strong coupling behavior to string
theory in AdS_5xS^5, finding precise agreement. We pay particular attention to
the case in which the local operators have large R-charge J \sim sqrt{lambda}
at strong coupling.Comment: 50 pages, 9 figures. v2: minor changes, references adde
Training deep neural density estimators to identify mechanistic models of neural dynamics
Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics
Unitarity of noncommutative field theories from string theory
We improve the study of the lack of perturbative unitarity of noncommutative
space-time quantum field theories derived from open string theory in electric
backgrounds, enforcing the universality of the mechanism by which a tachyonic
branch cut appears when the Seiberg-Witten limit freezes the string in an
unstable vacuum. The main example is realized in the context of the on-shell
four-tachyon amplitude of the bosonic string, and the dependence of the
phenomenon on the brane-worldvolume dimension is analysed. We discuss the
possibility of a proof in superstring theory, and finally mention the NCOS
limit in this framework.Comment: 8 pages, no figures. Work done in collaboration with A. Bassetto and
R. Valandro (Padua Univ.). Submitted for the proceedings of the conference
"Spacetime and Fundamental Interactions: Quantum Aspects. A conference to
honour A.P.Balachandran's 65th birthday", Vietri, 26-31 May 200
The light-cone gauge and the calculation of the two-loop splitting functions
We present calculations of next-to-leading order QCD splitting functions,
employing the light-cone gauge method of Curci, Furmanski, and Petronzio (CFP).
In contrast to the `principal-value' prescription used in the original CFP
paper for dealing with the poles of the light-cone gauge gluon propagator, we
adopt the Mandelstam-Leibbrandt prescription which is known to have a solid
field-theoretical foundation. We find that indeed the calculation using this
prescription is conceptionally clear and avoids the somewhat dubious
manipulations of the spurious poles required when the principal-value method is
applied. We reproduce the well-known results for the flavour non-singlet
splitting function and the N_C^2 part of the gluon-to-gluon singlet splitting
function, which are the most complicated ones, and which provide an exhaustive
test of the ML prescription. We also discuss in some detail the x=1 endpoint
contributions to the splitting functions.Comment: 41 Pages, LaTeX, 8 figures and tables as eps file
Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
A general framework is presented for the renormalization of Hamiltonians via
a similarity transformation. Divergences in the similarity flow equations may
be handled with dimensional regularization in this approach, and the resulting
effective Hamiltonian is finite since states well-separated in energy are
uncoupled. Specific schemes developed several years ago by Glazek and Wilson
and contemporaneously by Wegner correspond to particular choices within this
framework, and the relative merits of such choices are discussed from this
vantage point. It is shown that a scheme for the transformation of Hamiltonians
introduced by Dyson in the early 1950's also corresponds to a particular choice
within the similarity renormalization framework, and it is argued that Dyson's
scheme is preferable to the others for ease of computation. As an example, it
is shown how a logarithmically confining potential arises simply at second
order in light-front QCD within Dyson's scheme, a result found previously for
other similarity renormalization schemes. Steps toward higher order and
nonperturbative calculations are outlined. In particular, a set of equations
analogous to Dyson-Schwinger equations is developed.Comment: REVTex, 32 pages, 7 figures (corrected references
The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
We construct a generalized cusped Wilson loop operator in N = 6 super
Chern-Simons-matter theories which is locally invariant under half of the
supercharges. It depends on two parameters and interpolates smoothly between
the 1/2 BPS line or circle and a pair of antiparallel lines, representing a
natural generalization of the quark-antiquark potential in ABJ(M) theories. For
particular choices of the parameters we obtain 1/6 BPS configurations that,
mapped on S^2 by a conformal transformation, realize a three-dimensional
analogue of the wedge DGRT Wilson loop of N = 4. The cusp couples, in addition
to the gauge and scalar fields of the theory, also to the fermions in the
bifundamental representation of the U(N)xU(M) gauge group and its expectation
value is expressed as the holonomy of a suitable superconnection. We discuss
the definition of these observables in terms of traces and the role of the
boundary conditions of fermions along the loop. We perform a complete two-loop
analysis, obtaining an explicit result for the generalized cusp at the second
non-trivial order, from which we read off the interaction potential between
heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility
to explore in the three-dimensional case the connection between localization
properties and integrability, recently advocated in D = 4.Comment: 53 pages, 10 figures, added references, this is the version appeared
on JHE
Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
We re-examine the perturbative properties of four-dimensional non-commutative
QED by extending the pinch techniques to the theta-deformed case. The explicit
independence of the pinched gluon self-energy from gauge-fixing parameters, and
the absence of unphysical thresholds in the resummed propagators permits a
complete check of the optical theorem for the off-shell two-point function. The
known anomalous (tachyonic) dispersion relations are recovered within this
framework, as well as their improved version in the (softly broken) SUSY case.
These applications should be considered as a first step in constructing
gauge-invariant truncations of the Schwinger-Dyson equations in the
non-commutative case. An interesting result of our formalism appears when
considering the theory in two dimensions: we observe a finite gauge-invariant
contribution to the photon mass because of a novel incarnation of IR/UV mixing,
which survives the commutative limit when matter is present.Comment: 30 pages, 2 eps figure, uses axodraw. Citations adde
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