1,952 research outputs found
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
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
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
Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding
Certain topological invariants of the moduli space of gravitational
instantons are defined and studied. Several amplitudes of two and four
dimensional topological gravity are computed. A notion of puncture in four
dimensions, that is particularly meaningful in the class of Weyl instantons, is
introduced. The topological embedding, a theoretical framework for constructing
physical amplitudes that are well-defined order by order in perturbation theory
around instantons, is explicitly applied to the computation of the correlation
functions of Dirac fermions in a punctured gravitational background, as well as
to the most general QED and QCD amplitude. Various alternatives are worked out,
discussed and compared. The quantum background affects the propagation by
generating a certain effective ``quantum'' metric. The topological embedding
could represent a new chapter of quantum field theory.Comment: LaTeX, 18 pages, no figur
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
A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT_4
We discuss several aspects of superconformal field theories in four
dimensions (CFT_4), in the context of electric-magnetic duality. We analyse the
behaviour of anomalous currents under RG flow to a conformal fixed point in
N=1, D=4 supersymmetric gauge theories. We prove that the anomalous dimension
of the Konishi current is related to the slope of the beta function at the
critical point. We extend the duality map to the (nonchiral) Konishi current.
As a byproduct we compute the slope of the beta function in the strong coupling
regime. We note that the OPE of with itself does not close, but
mixes with a special additional operator which in general is the
Konishi current. We discuss the implications of this fact in generic
interacting conformal theories. In particular, a SCFT_4 seems to be naturally
equipped with a privileged off-critical deformation and this allows us
to argue that electric-magnetic duality can be extended to a neighborhood of
the critical point. We also stress that in SCFT_4 there are two central
charges, c and c', associated with the stress tensor and ,
respectively; c and c' allow us to count both the vector multiplet and the
matter multiplet effective degrees of freedom of the theory.Comment: harvmac tex, 28 pages, 3 figures. Version to be published in Nucl.
Phys.
Covariant Pauli-Villars Regularization of Quantum Gravity at the One Loop Order
We study a regularization of the Pauli-Villars kind of the one loop
gravitational divergences in any dimension. The Pauli-Villars fields are
massive particles coupled to gravity in a covariant and nonminimal way, namely
one real tensor and one complex vector. The gauge is fixed by means of the
unusual gauge-fixing that gives the same effective action as in the context of
the background field method. Indeed, with the background field method it is
simple to see that the regularization effectively works. On the other hand, we
show that in the usual formalism (non background) the regularization cannot
work with each gauge-fixing.In particular, it does not work with the usual one.
Moreover, we show that, under a suitable choice of the Pauli-Villars
coefficients, the terms divergent in the Pauli-Villars masses can be corrected
by the Pauli-Villars fields themselves. In dimension four, there is no need to
add counterterms quadratic in the curvature tensor to the Einstein action
(which would be equivalent to the introduction of new coupling constants). The
technique also works when matter is coupled to gravity. We discuss the possible
consequences of this approach, in particular the renormalization of Newton's
coupling constant and the appearance of two parameters in the effective action,
that seem to have physical implications.Comment: 26 pages, LaTeX, SISSA/ISAS 73/93/E
Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
For quantum field theories that flow between ultraviolet and infrared fixed
points, central functions, defined from two-point correlators of the stress
tensor and conserved currents, interpolate between central charges of the UV
and IR critical theories. We develop techniques that allow one to calculate the
flows of the central charges and that of the Euler trace anomaly coefficient in
a general N=1 supersymmetric gauge theory. Exact, explicit formulas for
gauge theories in the conformal window are given and analysed. The
Euler anomaly coefficient always satisfies the inequality .
This is new evidence in strongly coupled theories that this quantity satisfies
a four-dimensional analogue of the -theorem, supporting the idea of
irreversibility of the RG flow. Various other implications are discussed.Comment: latex, 27 page
ALE manifolds and Conformal Field Theory
We address the problem of constructing the family of (4,4) theories
associated with the sigma-model on a parametrized family of
Asymptotically Locally Euclidean (ALE) manifolds. We rely on the ADE
classification of these manifolds and on their construction as HyperK\"ahler
quotients, due to Kronheimer.
So doing we are able to define the family of (4,4) theories corresponding to
a family of ALE manifolds as the deformation of a solvable
orbifold conformal field-theory, being a
Kleinian group. We discuss the relation among the algebraic structure
underlying the topological and metric properties of self-dual 4-manifolds and
the algebraic properties of non-rational (4,4)-theories admitting an infinite
spectrum of primary fields. In particular, we identify the Hirzebruch signature
with the dimension of the local polynomial ring {\cal R}=\o {{\bf
C}[x,y,z]}{\partial W} associated with the ADE singularity, with the number of
non-trivial conjugacy classes in the corresponding Kleinian group and with the
number of short representations of the (4,4)-theory minus four.Comment: 48 pages, Latex, SISSA/44/92/EP, IFUM/443/F
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