29 research outputs found
Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals
We consider general aspects of the realization of R and non-R flavor
symmetries in the AdS_5 x H_5 dual of 4d N=1 superconformal field theories. We
find a general prescription for computing the charges under these symmetries
for baryonic operators, which uses only topological information (intersection
numbers) on H_5. We find and discuss a new correspondence between the nodes of
the SCFT quiver diagrams and certain divisors in the associated geometry. We
also discuss connections between the non-R flavor symmetries and the enhanced
gauge symmetries in non-conformal theories obtained by adding wrapped branes.Comment: 23 pages, 6 figures. v2: added comment
Exploring the 4d Superconformal Zoo
We discuss a new constraint for determining the superconformal U(1)_R
symmetry of 4d N=1 SCFTs: It is the unique one which locally maximizes a(R) =
3Tr R^3-Tr R. This constraint comes close to proving the conjectured
"a-theorem" for N=1 SCFTs. Using this "a-maximization", exact results can now
be obtained for previously inaccessible 4d N=1 SCFTs. We apply this method to a
rich class of examples: 4d N=1 SQCD with added matter chiral superfields in the
adjoint representation. We classify a zoo of SCFTs, finding that Arnold's ADE
singularity classification arises in classifying these theories via all
possible relevant Landau-Ginzburg superpotentials. We verify that all RG flows
are indeed compatible with the "a-theorem" conjecture, a_{IR}<a_{UV}, in every
caseComment: QTS '03 conference proceeding
N=1 RG Flows, Product Groups, and a-Maximization
We explore new IR phenomena and dualities, arising for product groups, in the
context of N=1 supersymmetric gauge theories. The RG running of the multiple
couplings can radically affect each other. For example, an otherwise IR
interacting coupling can be driven to be instead IR free by an arbitrarily
small, but non-zero, initial value of another coupling. Or an otherwise IR free
coupling can be driven to be instead IR interacting by an arbitrarily small
non-zero initial value of another coupling. We explore these and other
phenomena in N=1 examples, where exact results can be obtained using
a-maximization. We also explore the various possible dual gauge theories, e.g.
by dualizing one gauge group with the other treated as a weakly gauged flavor
symmetry, along with previously proposed duals for the theories deformed by
A_k-type Landau-Ginzburg superpotentials. We note that this latter duality, and
all similar duality examples, always have non-empty superconformal windows,
within which both the electric and dual A_k superpotentials are relevant.Comment: 36 pages, 8 figure
The Exact Superconformal R-Symmetry Maximizes a
An exact and general solution is presented for a previously open problem. We
show that the superconformal R-symmetry of any 4d SCFT is exactly and uniquely
determined by a maximization principle: it is the R-symmetry, among all
possibilities, which (locally) maximizes the combination of 't Hooft anomalies
a_{trial}(R) \equiv (9 Tr R^3-3 Tr R)/32. The maximal value of a_{trial} is
then, by a result of Anselmi et. al., the central charge \it{a} of the SCFT.
Our a_{trial} maximization principle almost immediately ensures that the
central charge \it{a} decreases upon any RG flow, since relevant deformations
force a_{trial} to be maximized over a subset of the previously possible
R-symmetries. Using a_{trial} maximization, we find the exact superconformal
R-symmetry (and thus the exact anomalous dimensions of all chiral operators) in
a variety of previously mysterious 4d N=1 SCFTs. As a check, we verify that our
exact results reproduce the perturbative anomalous dimensions in all
perturbatively accessible RG fixed points. Our result implies that N =1 SCFTs
are algebraic: the exact scaling dimensions of all chiral primary operators,
and the central charges \it{a} and \it{c}, are always algebraic numbers.Comment: 23 pages, 1 figure. v2: added comments. v3: added comment
RG Fixed Points and Flows in SQCD with Adjoints
We map out and explore the zoo of possible 4d N=1 superconformal theories
which are obtained as RG fixed points of N=1 SQCD with N_f fundamental and N_a
adjoint matter representations. Using "a-maximization," we obtain exact
operator dimensions at all RG fixed points and classify all relevant,
Landau-Ginzburg type, adjoint superpotential deformations. Such deformations
can be used to RG flow to new SCFTs, which are then similarly analyzed.
Remarkably, the resulting 4d SCFT classification coincides with Arnold's ADE
singularity classification. The exact superconformal R-charge and the central
charge a are computed for all of these theories. RG flows between the different
fixed points are analyzed, and all flows are verified to be compatible with the
conjectured a-theorem.Comment: 59 pages, 29 figure
Comments on Unstable Branes
We argue that type II string theories contain unstable NS4 branes, which
descend from a conjectured unstable M4 brane of M-theory. Assuming that an M2
brane can arise in M5 brane/anti-brane annihilation, the unstable M4 brane, and
also an unstable M3 brane, must exist as sphalerons. We compare the tensions of
the unstable NS4 branes, M4 brane, and related type II unstable D-branes, and
present 11d supergravity solutions for unstable Mp branes for all p. We study
the Z_2 gauge symmetry on the worldvolume of unstable branes, and argue that it
can never be unbroken in the presence of lower brane charge.Comment: 16 page
The Secret Gauging of Flavor Symmetries in Noncommutative QFT
We show that flavor 't Hooft anomalies automatically vanish in noncommutative
field theories which are obtained from string theory in the decoupling limit.
We claim that this is because the flavor symmetries are secretly local, because
of coupling to closed string bulk modes. An example is the SU(4) R-symmetry of
N=4 D=4 NCSYM. The gauge fields, along with all closed string bulk modes, are
not on-shell external states but do appear as off-shell intermediate states in
non-planar processes; these closed string modes are thereby holographically
encoded in the NCFT.Comment: 11 pages. LaTe
The Exact Superconformal R-symmetry Minimizes
We present a new, general constraint which, in principle, determines the
superconformal symmetry of 4d SCFTs, and also 3d
SCFTs. Among all possibilities, the superconformal is that which
minimizes the coefficient, , of its two-point function.
Equivalently, the superconformal is the unique one with vanishing
two-point function with every non-R flavor symmetry. For 4d SCFTs,
minimization gives an alternative to a-maximization.
minimization also applies in 3d, where no condition for determining the
superconformal had been previously known. Unfortunately, this
constraint seems impractical to implement for interacting field theories. But
it can be readily implemented in the AdS geometry for SCFTs with AdS duals.Comment: 18 page
Evidence for the Strongest Version of the 4d a-Theorem, via a-Maximization Along RG Flows
In earlier work, we (KI and BW) gave a two line "almost proof" (for
supersymmetric RG flows) of the weakest form of the conjectured 4d a-theorem,
that a_{IR}<a_{UV}, using our result that the exact superconformal R-symmetry
of 4d SCFTs maximizes a=3Tr R^3-Tr R. The proof was incomplete because of two
identified loopholes: theories with accidental symmetries, and the fact that
it's only a local maximum of \it{a}. Here we discuss and extend a proposal of
Kutasov (which helps close the latter loophole) in which a-maximization is
generalized away from the endpoints of the RG flow, with Lagrange multipliers
that are conjectured to be identified with the running coupling constants.
a-maximization then yields a monotonically decreasing "a-function" along the RG
flow to the IR. As we discuss, this proposal in fact suggests the strongest
version of the a-theorem: that 4d RG flows are gradient flows of an a-function,
with positive definite metric. In the perturbative limit, the RG flow metric
thus obtained is shown to agree precisely with that found by very different
computations by Osborn and collaborators. As examples, we discuss a new class
of 4d SCFTs, along with their dual descriptions and IR phases, obtained from
SQCD by coupling some of the flavors to added singlets.Comment: 36 pages, 6 figures. v2: added referenc