10 research outputs found
Counting BPS operators in N=4 SYM
The free field partition function for a generic U(N) gauge theory, where the
fundamental fields transform in the adjoint representation, is analysed in
terms of symmetric polynomial techniques. It is shown by these means how this
is related to the cycle polynomial for the symmetric group and how the large N
result may be easily recovered. Higher order corrections for finite N are also
discussed in terms of symmetric group characters. For finite N, the partition
function involving a single bosonic fundamental field is recovered and explicit
counting of multi-trace quarter BPS operators in free \N=4 super Yang Mills
discussed, including a general result for large N. The partition function for
BPS operators in the chiral ring of \N=4 super Yang Mills is analysed in terms
of plane partitions. Asymptotic counting of BPS primary operators with
differing R-symmetry charges is discussed in both free \N=4 super Yang Mills
and in the chiral ring. Also, general and explicit expressions are derived for
SU(2) gauge theory partition functions, when the fundamental fields transform
in the adjoint, for free field theory.Comment: 38 pages, uses harvmac, v.2. references added, typos corrected,
discussion of asymptotic counting included for more general chiral ring, v.3.
typos corrected, discussion for su(2) simplified, to be published in Nuclear
Physics
Higher-Spin Theory and Space-Time Metamorphoses
Introductory lectures on higher-spin gauge theory given at 7 Aegean workshop
on non-Einstein theories of gravity. The emphasis is on qualitative features of
the higher-spin gauge theory and peculiarities of its space-time
interpretation. In particular, it is explained that Riemannian geometry cannot
play a fundamental role in the higher-spin gauge theory. The higher-spin
symmetries are argued to occur at ultra high energy scales beyond the Planck
scale. This suggests that the higher-spin gauge theory can help to understand
Quantum Gravity. Various types of higher-spin dualities are briefly discussed.Comment: 37 pages, no figures; V2: references adde
An Index for 4 dimensional Super Conformal Theories
We present a trace formula for an index over the spectrum of four dimensional
superconformal field theories on time. Our index receives
contributions from states invariant under at least one supercharge and captures
all information -- that may be obtained purely from group theory -- about
protected short representations in 4 dimensional superconformal field theories.
In the case of the theory our index is a function of four
continuous variables. We compute it at weak coupling using gauge theory and at
strong coupling by summing over the spectrum of free massless particles in
and find perfect agreement at large and small charges.
Our index does not reproduce the entropy of supersymmetric black holes in
, but this is not a contradiction, as it differs qualitatively from the
partition function over supersymmetric states of the theory. We
note that entropy for some small supersymmetric black holes may be
reproduced via a D-brane counting involving giant gravitons. For big black
holes we find a qualitative (but not exact) agreement with the naive counting
of BPS states in the free Yang Mills theory. In this paper we also evaluate and
study the partition function over the chiral ring in the Yang
Mills theory.Comment: harvmac 40+16 pages, v3: references and table of contents added,
typos fixe
Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and Invariant Equations in Generalized (Super)Space
Realization of the conformal higher spin symmetry on the 4d massless field
supermultiplets is given. The self-conjugated supermultiplets, including the
linearized SYM theory, are considered in some detail. Duality
between non-unitary field-theoretical representations and the unitary
doubleton--type representations of the 4d conformal algebra is
formulated in terms of a Bogolyubov transform. The set of 4d massless fields of
all spins is shown to form a representation of .
The obtained results are extended to the generalized superspace invariant
under supersymmetries. World line particle interpretation of the
free higher spin theories in the invariant (super)space is
given. Compatible with unitarity free equations of motion in the
invariant (super)space are formulated. A conjecture on the chain of
dualities in the higher spin
gauge theories is proposed.Comment: Latex, 63 pages; no figures.V2 Typos corrected, References updated.
V3.Typos correced, references and an explanation on the relationship with
previous work in section 4 are added. The version to appear in Phys.Rev.
Holocene palaeochannels at SiSatchanalai, north-central Thailand: ages, significance and palaeoenvironmental indications
Elliptic Hypergeometry of Supersymmetric Dualities
We give a full list of known supersymmetric quantum field
theories related by the Seiberg electric-magnetic duality conjectures for
and gauge groups. Many of the presented dualities are
new, not considered earlier in the literature. For all these theories we
construct superconformal indices and express them in terms of elliptic
hypergeometric integrals. This gives a systematic extension of the related
Romelsberger and Dolan-Osborn results. Equality of indices in dual theories
leads to various identities for elliptic hypergeometric integrals. About half
of them were proven earlier, and another half represents new challenging
conjectures. In particular, we conjecture a dozen new elliptic beta integrals
on root systems extending the univariate elliptic beta integral discovered by
the first author.Comment: 70 pages, published versio