Weyl invariance, non-compact duality and conformal higher-derivative sigma models

We study a system of $n$ Abelian vector fields coupled to $\frac 12 n(n+1)$ complex scalars parametrising the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. This model is Weyl invariant and possesses the maximal non-compact duality group $\mathsf{Sp}(2n, {\mathbb R})$. Although both symmetries are anomalous in the quantum theory, they should be respected by the logarithmic divergent term (the ``induced action'') of the effective action obtained by integrating out the vector fields. We compute this induced action and demonstrate its Weyl and $\mathsf{Sp}(2n, {\mathbb R})$ invariance. The resulting conformal higher-derivative $\sigma$-model on $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$ is generalised to the cases where the fields take their values in (i) an arbitrary K\"ahler space; and (ii) an arbitrary Riemannian manifold. In both cases, the $\sigma$-model Lagrangian generates a Weyl anomaly satisfying the Wess-Zumino consistency condition.Comment: 24 page

The SU(N) Matrix Model at Two Loops

Multi-loop calculations of the effective action for the matrix model are important for carrying out tests of the conjectured relationship of the matrix model to the low energy description of M-theory. In particular, comparison with N-graviton scattering amplitudes in eleven-dimensional supergravity requires the calculation of the effective action for the matrix model with gauge group SU(N). A framework for carrying out such calculations at two loops is established in this paper. The two-loop effective action is explicitly computed for a background corresponding to the scattering of a single D0-brane from a stack of N-1 D0-branes, and the results are shown to agree with known results in the case N=2.Comment: 30 pages, 1 figure; v2 - typos corrected, references update

Higher order contributions to the effective action of N=2 super Yang-Mills

We apply heat kernel techniques in N=1 superspace to compute the one-loop effective action to order $F^5$ for chiral superfields coupled to a non-Abelian super Yang-Mills background. The results, when combined with those of hep-th/0210146, yield the one-loop effective action to order $F^5$ for any N=2 super Yang-Mills theory coupled to matter hypermultiplets.Comment: 23 pages, references adde

Higher order contributions to the effective action of N=4 super Yang-Mills

The one-loop low-energy effective action for non-Abelian N=4 supersymmetric Yang-Mills theory is computed to order $F^6$ by use of heat kernel techniques in N=1 superspace. At the component level, the $F^5$ terms are found to be consistent with the form of the non-Abelian Born-Infeld action computed to this order by superstring methods. The $F^6$ terms will be of importance for comparison with superstring calculations.Comment: 23 pages, JHEP style, references adde

A chromosome conformation capture ordered sequence of the barley genome

201

Effective actions in supersymmetric gauge theories: heat kernels for non-minimal operators

Abstract We study the quantum dynamics of a system of n Abelian N $$\mathcal{N}$$ = 1 vector multiplets coupled to 1 2 n n + 1 $$\frac{1}{2}n\left(n+1\right)$$ chiral multiplets which parametrise the Hermitian symmetric space Sp(2n, ℝ)/U(n). In the presence of supergravity, this model is super-Weyl invariant and possesses the maximal non-compact duality group Sp(2n, ℝ) at the classical level. These symmetries should be respected by the logarithmically divergent term (the “induced action”) of the effective action obtained by integrating out the vector multiplets. In computing the effective action, one has to deal with non-minimal operators for which the known heat kernel techniques are not directly applicable, even in flat (super)space. In this paper we develop a method to compute the induced action in Minkowski superspace. The induced action is derived in closed form and has a simple structure. It is a higher-derivative superconformal sigma model on Sp(2n, ℝ)/U(n). The obtained N $$\mathcal{N}$$ = 1 results are generalised to the case of N $$\mathcal{N}$$ = 2 local supersymmetry: a system of n Abelian N $$\mathcal{N}$$ = 2 vector multiplets coupled to N $$\mathcal{N}$$ = 2 chiral multiplets X I parametrising Sp(2n, ℝ)/U(n). The induced action is shown to be proportional to ∫ d 4 x d 4 θ d 4 θ ¯ E K X X ¯ $$\int {\textrm{d}}^4x{\textrm{d}}^4\theta {\textrm{d}}^4\overline{\theta}E\mathfrak{K}\left(X,\overline{X}\right)$$ , where K X X ¯ $$\mathfrak{K}\left(X,\overline{X}\right)$$ is the Kähler potential for Sp(2n, ℝ)/U(n). We also apply our method to compute DeWitt’s a 2 coefficients in some non-supersymmetric theories with non-minimal operators

Continuum Robot Arms Inspired by Cephalopods

In this paper, we describe our recent results in the development of a new class of soft, continuous backbone (“continuum”) robot manipulators. Our work is strongly motivated by the dexterous appendages found in cephalopods, particularly the arms and suckers of octopus, and the arms and tentacles of squid. Our ongoing investigation of these animals reveals interesting and unexpected functional aspects of their structure and behavior. The arrangement and dynamic operation of muscles and connective tissue observed in the arms of a variety of octopus species motivate the underlying design approach for our soft manipulators. These artificial manipulators feature biomimetic actuators, including artificial muscles based on both electro-active polymers (EAP) and pneumatic (McKibben) muscles. They feature a “clean ” continuous backbone design, redundant degrees of freedom, and exhibit significant compliance that provides novel operational capacities during environmental interaction and object manipulation. The unusual compliance and redundant degrees of freedom provide strong potential for application to delicate tasks in cluttered and/or unstructured environments. Our aim is to endow these compliant robotic mechanisms with the diverse and dexterous grasping behavior observed in octopuses. To this end, we are conducting fundamental research into the manipulation tactics, sensory biology, and neural control of octopuses. This work in turn leads to novel approaches to motion plannin