Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.Comment: latex, 27 page

Extremal Correlators in the AdS/CFT Correspondence

The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t \phi \phi$ and $s \phi \phi$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 \times S^5$.Comment: 26 pages, LateX, no figure

A sintering model for SiC(sub)w/Si3N4 composites

Presented is a model which suggests that it should be possible to pressureless sinter a SiC(sub w)/ Si3N4 composite to theoretical density. Prior failure to achieve complete densification by sintering is attributed to the use of compositions which result in a glass deficit. There is one basic premise for this model. The ratio of glass amount to surface area of nonglass constituents must be the same for both composite and sinterable monolithic Si3N4. This model suggests that whisker and grain sizes and whisker loading influence the glass amount necessary for successful sintering of composites. According to the model, a large glass amount will be necessary for successful sintering of these composites. However, grain boundary thicknesses in the composite will be less than those in the analogous monolithic materials. This suggests that good high temperature strength may still be attained. A recent report supports the predictions of the model

Slurry-pressing consolidation of silicon nitride

A baseline slurry-pressing method for a silicon nitride material is developed. The Si3N4 composition contained 5.8 wt percent SiO2 and 6.4 wt percent Y2O3. Slurry-pressing variables included volume percent solids, application of ultrasonic energy, and pH. Twenty vol percent slurry-pressed material was approximately 11 percent stronger than both 30 vol percent slurry-pressed and dry-pressed materials. The Student's t-test showed the difference to be significant at the 99 percent confidence level. Twenty volume percent (300 h) slurry-pressed test bars exhibited strengths as high as 980 MPa. Large, columnar beta-Si3N4 grains caused failure in the highest strength specimens. The improved strength correlated with better structural uniformity as determined by radiography, optical microscopy, and image analysis

Renormalisation of the Nonperturbative Thermal Pressure

We show how the fully resummed thermal pressure is rendered ultraviolet finite by standard zero-temperature renormalisation. The analysis is developed in a 6-dimensional scalar model that mimics QED and has $N$ flavours. The $N\to\infty$ limit of the model can be calculated completely. At a critical temperature, one of the degrees of freedom has vanishing screening mass like the transverse gauge bosons in four-dimensional finite-temperature perturbation theory. The renormalised nonperturbative interaction pressure of this model is evaluated numerically.Comment: 27 pages, plain tex, with 10 figures embedded using eps

Brane Worlds in Collision

We obtain an exact solution of the supergravity equations of motion in which the four-dimensional observed universe is one of a number of colliding D3-branes in a Calabi-Yau background. The collision results in the ten-dimensional spacetime splitting into disconnected regions, bounded by curvature singularities. However, near the D3-branes the metric remains static during and after the collision. We also obtain a general class of solutions representing $p$-brane collisions in arbitrary dimensions, including one in which the universe ends with the mutual annihilation of a positive-tension and negative-tension 3-brane.Comment: RevTex, 4 pages, 1 figure, typos and minor errors correcte

On the massless contributions to the vacuum polarization of heavy quarks

Recently Groote and Pivovarov have given notice of a possible fault in the use of sum rules involving two-point correlation functions to extract information on heavy quark parameters, due to the presence of massless contributions that invalidate the construction of moments of the spectral densities. Here we show how to circumvent this problem through a new definition of the moments, providing an infrared safe and consistent procedure.Comment: 1+9 pages, 3 figures. Discussion on QCD sum rules applications added. Conclusions unchanged. Version to be published in Journal of Physics

27/32

We show that when an N=2 SCFT flows to an N=1 SCFT via giving a mass to the adjoint chiral superfield in a vector multiplet with marginal coupling, the central charges a and c of the N=2 theory are related to those of the N=1 theory by a universal linear transformation. In the large N limit, this relationship implies that the central charges obey a_IR/a_UV=c_IR/c_UV=27/32. This gives a physical explanation to many examples of this number found in the literature, and also suggests the existence of a flow between some theories not previously thought to be connected.Comment: 3 pages. v2: references added, minor typos correcte

The dual of Janus -:- an interface CFT

We propose and study a specific gauge theory dual of the smooth, non-supersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary Tr(X^I X^J) and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g^2_{YM}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value are protected to all orders in g^2_{YM}N, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. SO(3,2) symmetry requires vanishing vacuum energy, =0, and this is confirmed in first order in the discontinuity.Comment: 24 pages, 1 figure; references adde