380 research outputs found
A Bound on the Superpotential
We prove a general bound on the superpotential in theories with broken
supersymmetry and broken R-symmetry, 2|W|< f_a F, where f_a and F are the
R-axion and Goldstino decay constants, respectively. The bound holds for weakly
coupled as well as strongly coupled theories, thereby providing an exact result
in theories with broken supersymmetry. We briefly discuss several possible
applications.Comment: 20 page
Goldstinos, Supercurrents and Metastable SUSY Breaking in N=2 Supersymmetric Gauge Theories
We construct an N=2 supersymmetric generalization of the N=1 supercurrent
formalism of Komargodski and Seiberg (KS) and use it to show that N=2 theories
with linear superconformal anomalies cannot break SUSY under certain broad
assumptions. This result suggests that there are no metastable SUSY breaking
vacua in a large class of theories that includes N=2 Super Yang-Mills (SYM).Comment: 19 pages; minor revisions; JHEP versio
Three form potential in (special) minimal supergravity superspace and supermembrane supercurrent
This contribution begins the study of the complete superfield Lagrangian
description of the interacting system of D=4 N=1 supergravity (SUGRA) and
supermembrane. Firstly, we review a 'three form supergravity' by Ovrut and
Waldram, which we prefer to call 'special minimal supergravity'. This off-shell
formulation of simple SUGRA is appropriate for our purposes as the
supermembrane action contains the so-called Wess-Zumino term given by the
integral over a three form potential in superspace, C3. We describe this
formulation in the frame of Wess--Zumino superfield approach, showing how the
basic variations of minimal SUGRA are restricted by the conditions of the
existence of a three-form potential C3 in its superspace. In this language the
effect of dynamical generation of cosmological constant, known to be
characteristic for this formulation of SUGRA, appears in its superfield form,
first described by Ogievetsky and Sokatchev in their formulation of SUGRA as a
theory of axial vector superfield. Secondly, we vary the supermembrane action
with respect to the special minimal SUGRA superfields (basic variations) and
obtain the supercurrent superfields as well as the supergravity superfield
equations with the supermembrane contributions.Comment: 18 pages, no figures. V2: Important references added. The abstract
and presentation have been changed to reflect the overloop with that.
Submitted to the QTS7 Proceedings. J. Phys. style use
Limit Cycles and Conformal Invariance
There is a widely held belief that conformal field theories (CFTs) require
zero beta functions. Nevertheless, the work of Jack and Osborn implies that the
beta functions are not actually the quantites that decide conformality, but
until recently no such behavior had been exhibited. Our recent work has led to
the discovery of CFTs with nonzero beta functions, more precisely CFTs that
live on recurrent trajectories, e.g., limit cycles, of the beta-function vector
field. To demonstrate this we study the S function of Jack and Osborn. We use
Weyl consistency conditions to show that it vanishes at fixed points and agrees
with the generator Q of limit cycles on them. Moreover, we compute S to third
order in perturbation theory, and explicitly verify that it agrees with our
previous determinations of Q. A byproduct of our analysis is that, in
perturbation theory, unitarity and scale invariance imply conformal invariance
in four-dimensional quantum field theories. Finally, we study some properties
of these new, "cyclic" CFTs, and point out that the a-theorem still governs the
asymptotic behavior of renormalization-group flows.Comment: 31 pages, 4 figures. Expanded introduction to make clear that cycles
discussed in this work are not associated with unitary theories that are
scale but not conformally invarian
General Messenger Gauge Mediation
We discuss theories of gauge mediation in which the hidden sector consists of
two subsectors which are weakly coupled to each other. One sector is made up of
messengers and the other breaks supersymmetry. Each sector by itself may be
strongly coupled. We provide a unifying framework for such theories and discuss
their predictions in different settings. We show how this framework
incorporates all known models of messengers. In the case of weakly-coupled
messengers interacting with spurions through the superpotential, we prove that
the sfermion mass-squared is positive, and furthermore, that there is a lower
bound on the ratio of the sfermion mass to the gaugino mass.Comment: 37 pages; minor change
Scale without Conformal Invariance at Three Loops
We carry out a three-loop computation that establishes the existence of scale
without conformal invariance in dimensional regularization with the MS scheme
in d=4-epsilon spacetime dimensions. We also comment on the effects of scheme
changes in theories with many couplings, as well as in theories that live on
non-conformal scale-invariant renormalization group trajectories. Stability
properties of such trajectories are analyzed, revealing both attractive and
repulsive directions in a specific example. We explain how our results are in
accord with those of Jack & Osborn on a c-theorem in d=4 (and d=4-epsilon)
dimensions. Finally, we point out that limit cycles with turning points are
unlike limit cycles with continuous scale invariance.Comment: 21 pages, 3 figures, Erratum adde
Limit Cycles in Four Dimensions
We present an example of a limit cycle, i.e., a recurrent flow-line of the
beta-function vector field, in a unitary four-dimensional gauge theory. We thus
prove that beta functions of four-dimensional gauge theories do not produce
gradient flows. The limit cycle is established in perturbation theory with a
three-loop calculation which we describe in detail.Comment: 12 pages, 1 figure. Significant revision of the interpretation of our
result. Improved description of three-loop calculatio
Global Symmetries and D-Terms in Supersymmetric Field Theories
We study the role of D-terms in supersymmetry (SUSY) breaking. By carefully
analyzing the SUSY multiplets containing various conserved currents in theories
with global symmetries, we obtain a number of constraints on the
renormalization group flow in supersymmetric field theories. Under broad
assumptions, these results imply that there are no SUSY-breaking vacua, not
even metastable ones, with parametrically large D-terms. This explains the
absence of such D-terms in models of dynamical SUSY-breaking. There is,
however, a rich class of calculable models which generate comparable D-terms
and F-terms through a variety of non-perturbative effects; these D-terms can be
non-abelian. We give several explicit examples of such models, one of which is
a new calculable limit of the 3-2 model.Comment: 34 pages, 2 figures; reference added, minor change
The Constraints of Conformal Symmetry on RG Flows
If the coupling constants in QFT are promoted to functions of space-time, the
dependence of the path integral on these couplings is highly constrained by
conformal symmetry. We begin the present note by showing that this idea leads
to a new proof of Zamolodchikov's theorem. We then review how this simple
observation also leads to a derivation of the a-theorem. We exemplify the
general procedure in some interacting theories in four space-time dimensions.
We concentrate on Banks-Zaks and weakly relevant flows, which can be controlled
by ordinary and conformal perturbation theories, respectively. We compute
explicitly the dependence of the path integral on the coupling constants and
extract the change in the a-anomaly (this agrees with more conventional
computations of the same quantity). We also discuss some general properties of
the sum rule found in arXiv:1107.3987 and study it in several examples.Comment: 25 pages, 5 figure
The -theorem and the Asymptotics of 4D Quantum Field Theory
We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary
quantum field theory. Our main tool is a generalization of the
Komargodski-Schwimmer proof for the -theorem. We use this to rule out a
large class of renormalization group flows that do not asymptote to conformal
field theories in the UV and IR. We show that if the IR (UV) asymptotics is
described by perturbation theory, all beta functions must vanish faster than
as (). This implies that the
only possible asymptotics within perturbation theory is conformal field theory.
In particular, it rules out perturbative theories with scale but not conformal
invariance, which are equivalent to theories with renormalization group
pseudocycles. Our arguments hold even for theories with gravitational
anomalies. We also give a non-perturbative argument that excludes theories with
scale but not conformal invariance. This argument holds for theories in which
the stress-energy tensor is sufficiently nontrivial in a technical sense that
we make precise.Comment: 41 pages, 2 figures. v2: Arguments clarified, some side comments
corrected, connection to previous work by Jack and Osborn described,
conclusions unaffecte
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