Supersymmetric States in M5/M2 CFTs

We propose an exact, finite $N$ formula for the partition function over $1/4^{th}$ BPS states in the conformal field theory on the world volume of $N$ coincident M5 branes and $1/8^{th}$ BPS states in the theory of $N$ coincident M2 branes. We obtain our partition function by performing the radial quantization of the Coulomb Branches of these theories, and rederive the same formula from the quantization of supersymmetric giant and dual giant gravitons in $AdS_7 \times S^4$ and $AdS_4 \times S^7$. Our partition function is qualitatively similar to the analogous quantity in ${\cal N}=4$ Yang Mills. It reduces to the sum over supersymmetric multi gravitons at low energies, but deviates from this supergravity formula at energies that scale like a positive power of $N$.Comment: 24 pages, harvmac; v2 reference adde

Supergravity at the boundary of AdS supergravity

We give a general analysis of AdS boundary conditions for spin-3/2 Rarita-Schwinger fields and investigate boundary conditions preserving supersymmetry for a graviton multiplet in AdS_4. Linear Rarita-Schwinger fields in AdS_d are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range $0 \leq |m| < 1/2l_{AdS}$. We also demonstrate that mixed boundary conditions are allowed for larger masses when the inner product is "renormalized" accordingly with the action. We then use the results obtained for |m| = 1/l_{AdS} to explore supersymmetric boundary conditions for N = 1 AdS_4 supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We classify boundary conditions that preserve boundary supersymmetry or superconformal symmetry. Under the AdS/CFT dictionary, Neumann boundary conditions in d=4 supergravity correspond to gauging the superconformal group of the 3-dimensional CFT describing M2-branes, while N = 1 supersymmetric mixed boundary conditions couple the CFT to N = 1 superconformal topologically massive gravity.Comment: 23 pages, RevTe

Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent

The Moyal and Wick-Voros planes A^{M,V}_{\theta} are *-isomorphic. On each of these planes the Poincar\'e group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors. We show that the *-isomorphism T: A^M_{\theta} to A^V_{\theta} does not also map the corresponding twists of the Poincar\'e group algebra. The quantum field theories on these planes with twisted Poincar\'e-Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a non-trivial dependence on the non-commutative parameter is present for the Wick-Voros plane in a self-energy diagram whereas it is known to be absent on the Moyal plane (in the absence of gauge fields). Our results differ from these of (arXiv:0810.2095 [hep-th]) because of differences in the treatments of quantum field theories.Comment: 12 page

The Kepler problem and non commutativity

We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable corrections to the movement of the solar system. In this way, modifications in the physics of smaller scales implies modifications at large scales, something similar to the UV/IR mixing.Comment: 10 page

Elimination of IR/UV via Gravity in Noncommutative Field Theory

Models of particle physics with Noncommutative Geometry (NCG) generally suffer from a manifestly non-Wilsonian coupling of infrared and ultraviolet degrees of freedom known as the "IR/UV Problem" which would tend to compromise their phenomenological relevance. In this Letter we explicitly show how one may remedy this by coupling NCG to gravity. In the simplest scenario the Lagrangian gets multiplied by a nonconstant background metric; in $\phi-4$ theory the theorem that $\int d^4 x \phi \star \phi = \int d^4 x \phi^2$ is no longer true and the field propagator gets modified by a factor which depends on both NCG and the variation of the metric. A suitable limit of this factor as the propagating momentum gets asymptotically large then eradicates the IR/UV problem. With gravity and NCG coupled to each other, one might expect anti-symmetric components to arise in the metric. Cosmological implications of such are subsequently discussed.Comment: 6 pages; MPLA versio

Relaxing a constraint on the number of messengers in a low-scale gauge mediation

We propose a mechanism for relaxing a constraint on the number of messengers in low-scale gauge mediation models. The Landau pole problem for the standard-model gauge coupling constants in the low-scale gauge mediation can be circumvented by using our mechanism. An essential ingredient is a large positive anomalous dimension of messenger fields given by a large Yukawa coupling in a conformal field theory at high energies. The positive anomalous dimension reduces the contribution of the messengers to the beta function of the standard-model gauge couplings.Comment: 22pages; v2:explanations expanded in sec.3.2, reference adde

Indices for Superconformal Field Theories in 3,5 and 6 Dimensions

We present a trace formula for a Witten type Index for superconformal field theories in d=3,5 and 6 dimensions, generalizing a similar recent construction in d=4. We perform a detailed study of the decomposition of long representations into sums of short representations at the unitarity bound to demonstrate that our trace formula yields the most general index (i.e. quantity that is guaranteed to be protected by superconformal symmetry alone) for the corresponding superalgebras. Using the dual gravitational description, we compute our index for the theory on the world volume of N M2 and M5 branes in the large N limit. We also compute our index for recently constructed Chern Simons theories in three dimensions in the large N limit, and find that, in certain cases, this index undergoes a large N phase transition as a function of chemical potentials.Comment: a small typo corrected, 46 page

The Renormalization of Non-Commutative Field Theories in the Limit of Large Non-Commutativity

We show that renormalized non-commutative scalar field theories do not reduce to their planar sector in the limit of large non-commutativity. This follows from the fact that the RG equation of the Wilson-Polchinski type which describes the genus zero sector of non-commutative field theories couples generic planar amplitudes with non-planar amplitudes at exceptional values of the external momenta. We prove that the renormalization problem can be consistently restricted to this set of amplitudes. In the resulting renormalized theory non-planar divergences are treated as UV divergences requiring appropriate non-local counterterms. In 4 dimensions the model turns out to have one more relevant (non-planar) coupling than its commutative counterpart. This non-planar coupling is ``evanescent'': although in the massive (but not in the massless) case its contribution to planar amplitudes vanishes when the floating cut-off equals the renormalization scale, this coupling is needed to make the Wilsonian effective action UV finite at all values of the floating cut-off.Comment: 35 pages, 8 figures; typos correcte