5,780 research outputs found
Quantum Conformal Algebras and Closed Conformal Field Theory
We investigate the quantum conformal algebras of N=2 and N=1 supersymmetric
gauge theories. Phenomena occurring at strong coupling are analysed using the
Nachtmann theorem and very general, model-independent, arguments. The results
lead us to introduce a novel class of conformal field theories, identified by a
closed quantum conformal algebra. We conjecture that they are the exact
solution to the strongly coupled large-N_c limit of the open conformal field
theories. We study the basic properties of closed conformal field theory and
work out the operator product expansion of the conserved current multiplet T.
The OPE structure is uniquely determined by two central charges, c and a. The
multiplet T does not contain just the stress-tensor, but also R-currents and
finite mass operators. For this reason, the ratio c/a is different from 1. On
the other hand, an open algebra contains an infinite tower of non-conserved
currents, organized in pairs and singlets with respect to renormalization
mixing. T mixes with a second multiplet T* and the main consequence is that c
and a have different subleading corrections. The closed algebra simplifies
considerably at c=a, where it coincides with the N=4 one.Comment: 19 page
Towards the classification of conformal field theories in arbitrary even dimension
I identify the class of even-dimensional conformal field theories that is
most similar to two-dimensional conformal field theory. In this class the
formula, elaborated recently, for the irreversibility of the
renormalization-group flow applies also to massive flows. This implies a
prediction for the ratio between the coefficient of the Euler density in the
trace anomaly (charge a) and the stress-tensor two-point function (charge c).
More precisely, the trace anomaly in external gravity is quadratic in the Ricci
tensor and the Ricci scalar and contains a unique central charge. I check the
prediction in detail in four, six and eight dimensions, and then in arbitrary
even dimension.Comment: 9 page
A universal flow invariant in quantum field theory
A flow invariant is a quantity depending only on the UV and IR conformal
fixed points and not on the flow connecting them. Typically, its value is
related to the central charges a and c. In classically-conformal field
theories, scale invariance is broken by quantum effects and the flow invariant
a_{UV}-a_{IR} is measured by the area of the graph of the beta function between
the fixed points. There exists a theoretical explanation of this fact. On the
other hand, when scale invariance is broken at the classical level, it is
empirically known that the flow invariant equals c_{UV}-c_{IR} in massive
free-field theories, but a theoretical argument explaining why it is so is
still missing. A number of related open questions are answered here. A general
formula of the flow invariant is found, which holds also when the stress tensor
has improvement terms. The conditions under which the flow invariant equals
c_{UV}-c_{IR} are identified. Several non-unitary theories are used as a
laboratory, but the conclusions are general and an application to the Standard
Model is addressed. The analysis of the results suggests some new minimum
principles, which might point towards a better understanding of quantum field
theory.Comment: 28 pages, 3 figures; proof-corrected version for CQ
A note on the dimensional regularization of the Standard Model coupled with Quantum Gravity
In flat space, gamma5 and the epsilon tensor break the dimensionally
continued Lorentz symmetry, but propagators have fully Lorentz invariant
denominators. When the Standard Model is coupled with quantum gravity gamma5
breaks the continued local Lorentz symmetry. I show how to deform the Einstein
lagrangian and gauge-fix the residual local Lorentz symmetry so that the
propagators of the graviton, the ghosts and the BRST auxiliary fields have
fully Lorentz invariant denominators. This makes the calculation of Feynman
diagrams more efficient.Comment: 8 pages; v2: comment on first order formalism, PL
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
The Complete Form of N=2 Supergravity and its Place in the General Framework of D=4 N--Extended Supergravities
Relying on the geometrical set up of Special K\"ahler Geometry and
Quaternionic Geometry, which I discussed at length in my Lectures at the 1995
edition of this Spring School, I present here the recently obtained fully
general form of N=2 supergravity with completely arbitrary couplings. This
lagrangian has already been used in the literature to obtain various results:
notably the partial breaking of supersymmetry and various extremal black--hole
solutions. My emphasis, however, is only on providing the reader with a
completely explicit and ready to use component expression of the supergravity
action. All the details of the derivation are omitted but all the definitions
of the items entering the lagrangian and the supersymmetry transformation rules
are given.Comment: 11 pages, LaTeX espcrc2, Seminar at Trieste Spring School 199
A Note on the Holographic Beta and C Functions
The holographic RG flow in AdS/CFT correspondence naturally defines a
holographic scheme in which the central charge c and the beta function are
related by a universal formula. We perform some checks of that formula and we
compare it with quantum field theory expectations. We discuss alternative
definitions of the c-function. In particular, we compare, for a particular
supersymmetric flow, the holographic c-function with the central charge
computed directly from the two-point function of the stress-energy tensor.Comment: Version accepted for publication in Phys. Lett. B, expanded
introduction. 11 pages, 2 embedded eps figure
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
Gauged Hyperinstantons and Monopole Equations
The monopole equations in the dual abelian theory of the N=2 gauge-theory,
recently proposed by Witten as a new tool to study topological invariants, are
shown to be the simplest elements in a class of instanton equations that follow
from the improved topological twist mechanism introduced by the authors in
previous papers. When applied to the N=2 sigma-model, this twisting procedure
suggested the introduction of the so-called hyperinstantons, or triholomorphic
maps. When gauging the sigma-model by coupling it to the vector multiplet of a
gauge group G, one gets gauged hyperinstantons that reduce to the
Seiberg-Witten equations in the flat case and G=U(1). The deformation of the
self-duality condition on the gauge-field strength due to the
monopole-hyperinstanton is very similar to the deformation of the self-duality
condition on the Riemann curvature previously observed by the authors when the
hyperinstantons are coupled to topological gravity. In this paper the general
form of the hyperinstantonic equations coupled to both gravity and gauge
multiplets is presented.Comment: 13 pages, latex, no figures, [revision: a couple of references
reordered correctly
Gravitational Axial Anomaly for Four Dimensional Conformal Field Theories
We construct the three point function involving an axial vector current and
two energy-momentum tensors for four dimensional conformal field theories.
Conformal symmetry determines the form of this three point function uniquely up
to a constant factor if the necessary conservation conditions are imposed. The
gravitational axial anomaly present on a curved space background leads to a
non-zero contribution for the divergence of the axial current in this three
point function even on flat space. Using techniques related to differential
regularisation which guarantee that the energy-momentum tensor is conserved and
traceless, we calculate the anomaly in the three point function directly. In
this way we relate the overall coefficient of the three point function to the
scale of the gravitational axial anomaly. We check our results by applying them
to the examples of the fermion and photon axial currents.Comment: 15 pages, LaTex, no figures. Discussion of photon triangle anomaly
extended, references added. To appear in Nuclear Physics
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