55 research outputs found

### Lagrange Multipliers and Couplings in Supersymmetric Field Theory

In hep-th/0312098 it was argued that by extending the ``$a$-maximization'' of
hep-th/0304128 away from fixed points of the renormalization group, one can
compute the anomalous dimensions of chiral superfields along the flow, and
obtain a better understanding of the irreversibility of RG flow in four
dimensional supersymmetric field theory. According to this proposal, the role
of the running couplings is played by certain Lagrange multipliers that are
introduced in the construction. We show that one can choose a parametrization
of the space of couplings in which the Lagrange multipliers can indeed be
identified with the couplings, and discuss the consequences of this for weakly
coupled gauge theory.Comment: 13 pages, harvma

### Moduli Anomalies and Local Terms in the Operator Product Expansion

Local terms in the Operator Product Expansion in Superconformal Theories with
extended supersymmetry are identified. Assuming a factorized structure for
these terms their contributions are discussed.Comment: 24 pages, 2 figures, v2: footnote and reference adde

### Comments on the Algebraic Properties of Dilaton Actions

We study the relation between the dilaton action and sigma models for the
Goldstone bosons of the spontaneous breaking of the conformal group. We argue
that the relation requires that the sigma model is diffeomorphism invariant.
The origin of the WZW terms for the dilaton is clarified and it is shown that
in this approach the dilaton WZW term is necessarily accompanied by a Weyl
invariant term proposed before from holographic considerations.Comment: 19 page

### (8,0) Quantum mechanics and symmetry enhancement in type I' superstrings

The low-energy supersymmetric quantum mechanics describing D-particles in the
background of D8-branes and orientifold planes is analyzed in detail, including
a careful discussion of Gauss' law and normal ordering of operators. This
elucidates the mechanism that binds D-particles to an orientifold plane, in
accordance with the predictions of heterotic/type I duality. The ocurrence of
enhanced symmetries associated with massless bound states of a D-particle with
one orientifold plane is illustrated by the enhancement of $SO(14) \times U(1)$
to $E_8$ and $SO(12)\times U(1)$ to $E_7$ at strong type I' coupling.
Enhancement to higher-rank groups involves both orientifold planes. For
example, the enhanced $E_8 \times E_8 \times SU(2)$ symmetry at the self-dual
radius of the heterotic string is seen as the result of two D8-branes
coinciding midway between the orientifold planes, while the enhanced $SU(18)$
symmetry results from the coincidence of all sixteen D8-branes and $SO(34)$
when they also coincide with an orientifold plane. As a separate by-product,
the s-rule of brane-engineered gauge theories is derived by relating it through
a chain of dualities to the Pauli exclusion principle.Comment: 30 pages LaTeX, Five figures. Two references added as well as some
Comments in section4. v4: Missing backslashes added to four reference
citations

### Anomalies, Conformal Manifolds, and Spheres

The two-point function of exactly marginal operators leads to a universal
contribution to the trace anomaly in even dimensions. We study aspects of this
trace anomaly, emphasizing its interpretation as a sigma model, whose target
space M is the space of conformal field theories (a.k.a. the conformal
manifold). When the underlying quantum field theory is supersymmetric, this
sigma model has to be appropriately supersymmetrized. As examples, we consider
in some detail N=(2,2) and N=(0,2) supersymmetric theories in d=2 and N=2
supersymmetric theories in d=4. This reasoning leads to new information about
the conformal manifolds of these theories, for example, we show that the
manifold is Kahler-Hodge and we further argue that it has vanishing Kahler
class. For N=(2,2) theories in d=2 and N=2 theories in d=4 we also show that
the relation between the sphere partition function and the Kahler potential of
M follows immediately from the appropriate sigma models that we construct.
Along the way we find several examples of potential trace anomalies that obey
the Wess-Zumino consistency conditions, but can be ruled out by a more detailed
analysis.Comment: harvmac, 38 pages; references added and small clarification

### Remarks on Resonant Scalars in the AdS/CFT Correspondence

The special properties of scalars having a mass such that the two possible
dimensions of the dual scalar respect the unitarity and the
Breitenlohner-Freedman bounds and their ratio is integral (``resonant
scalars'') are studied in the AdS/CFT correspondence. The role of logarithmic
branches in the gravity theory is related to the existence of a trace anomaly
and to a marginal deformation in the Conformal Field Theory. The existence of
asymptotic charges for the conformal group in the gravity theory is interpreted
in terms of the properties of the corresponding CFT.Comment: 16 pages, 1 figur

### Universal Features of Holographic Anomalies

We study the mechanism by which gravitational actions reproduce the trace
anomalies of the holographically related conformal field theories. Two
universal features emerge: a) the ratios of type B trace anomalies in any even
dimension are independent of the gravitational action, being uniquely
determined by the underlying algebraic structure b) the normalization of the
type A and the overall normalization of the type B anomalies are given by
action dependent expressions with the dimension dependence completely fixed.Comment: 17 pages, harvma

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