Euclidean D-branes and higher-dimensional gauge theory

We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane---that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory---is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N_T = 2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G_2 holonomy.Comment: 23 pages (some changes in section 4.5 -- equations 27 and 28 change slightly) (missing bibliography added!

Conserved charges and supersymmetry in principal chiral and WZW models

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess-Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra modulo its Coxeter number, can be carried out irrespective of the coefficient of the Wess-Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension.Comment: LaTeX; 49 pages; v2: minor changes and additions to text and ref

Supersymmetric Yang-Mills, octonionic instantons and triholomorphic curves

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of ten-dimensional supersymmetric Yang-Mills theory. More precisely we show that the dimensional reduction of the (5+1)-dimensional supersymmetric sigma model with hyperkaehler (but otherwise arbitrary) target X to a four-dimensional hyperkaehler manifold M is a topological sigma model localising on the space of triholomorphic maps M -> X (or hyperinstantons). When X is the moduli space M_K of instantons on a four-dimensional hyperkaehler manifold K, this theory has an interpretation in terms of supersymmetric gauge theory. In this case, the topological sigma model can be understood as an adiabatic limit of the dimensional reduction of ten-dimensional supersymmetric Yang-Mills on the eight-dimensional manifold M x K of holonomy Sp(1) x Sp(1) in Spin(7), which is a cohomological theory localising on the moduli space of octonionic instantons.Comment: 26 pages, LaTeX2e (A comment and a corresponding acknowledgement added and a reference ammended

Conserved Charges in the Principal Chiral Model on a Supergroup

The classical principal chiral model in 1+1 dimensions with target space a compact Lie supergroup is investigated. It is shown how to construct a local conserved charge given an invariant tensor of the Lie superalgebra. We calculate the super-Poisson brackets of these currents and argue that they are finitely generated. We show how to derive an infinite number of local charges in involution. We demonstrate that these charges Poisson commute with the non-local charges of the model

Differential localization of LTA synthesis proteins and their interaction with the cell division machinery in Staphylococcus aureus

Lipoteichoic acid (LTA) is an important cell wall component of Gram-positive bacteria. In Staphylococcus aureus it consists of a polyglycerolphosphate-chain that is retained within the membrane via a glycolipid. Using an immunofluorescence approach, we show here that the LTA polymer is not surface exposed in S. aureus, as it can only be detected after digestion of the peptidoglycan layer. S. aureus mutants lacking LTA are enlarged and show aberrant positioning of septa, suggesting a link between LTA synthesis and the cell division process. Using a bacterial two-hybrid approach, we show that the three key LTA synthesis proteins, YpfP and LtaA, involved in glycolipid production, and LtaS, required for LTA backbone synthesis, interact with one another. All three proteins also interacted with numerous cell division and peptidoglycan synthesis proteins, suggesting the formation of a multi-enzyme complex and providing further evidence for the co-ordination of these processes. When assessed by fluorescence microscopy, YpfP and LtaA fluorescent protein fusions localized to the membrane while the LtaS enzyme accumulated at the cell division site. These data support a model whereby LTA backbone synthesis proceeds in S. aureus at the division site in co-ordination with cell division, while glycolipid synthesis takes place throughout the membrane

The Octonionic Membrane

We generalize the supermembrane solution of D=11 supergravity by permitting the 4-form $G$ to be either self-dual or anti-self-dual in the eight dimensions transverse to the membrane. After analyzing the supergravity field equations directly, and also discussing necessary conditions for unbroken supersymmetry, we focus on two specific, related solutions. The self-dual solution is not asymptotically flat. The anti-self-dual solution is asymptotically flat, has finite mass per unit area and saturates the same mass=charge Bogomolnyi bound as the usual supermembrane. Nevertheless, neither solution preserves any supersymmetry. Both solutions involve the octonionic structure constants but, perhaps surprisingly, they are unrelated to the octonionic instanton 2-form $F$, for which $TrF \wedge F$ is neither self-dual nor anti-self-dual.Comment: 17 pages, Latex; enhanced discussion on supersymmetry, some references adde

Surgical trial design for incorporating the effects of learning: what is the current methodological guidance, and is it sufficient?

Background Surgical interventions are complex. Key elements of this complexity are the surgeon and their learning curve. They pose methodological challenges in the design, analysis and interpretation of surgical RCTs. We identify, summarise, and critically examine current guidance about how to incorporate learning curves in the design and analysis of RCTs in surgery. Examining current guidance Current guidance presumes that randomisation must be between levels of just one treatment component, and that the evaluation of comparative effectiveness will be made via the average treatment effect (ATE). It considers how learning effects affect the ATE, and suggests solutions which seek to define the target population such that the ATE is a meaningful quantity to guide practice. We argue that these are solutions to a flawed formulation of the problem, and are inadequate for policymaking in this setting. Reformulating the problem The premise that surgical RCTs are limited to single-component comparisons, evaluated via the ATE, has skewed the methodological discussion. Forcing a multi-component intervention, such as surgery, into the framework of the conventional RCT design ignores its factorial nature. We briefly discuss the multiphase optimisation strategy (MOST), which for a Stage 3 trial would endorse a factorial design. This would provide a wealth of information to inform nuanced policy but would likely be infeasible in this setting. We discuss in more depth the benefits of targeting the ATE conditional on operating surgeon experience (CATE). The value of estimating the CATE for exploring learning effects has been previously recognised, but with discussion limited to analysis methods only. The robustness and precision of such analyses can be ensured via the trial design, and we argue that trial designs targeting CATE represent a clear gap in current guidance. Conclusion Trial designs that facilitate robust, precise estimation of the CATE would allow for more nuanced policymaking, leading to patient benefit. No such designs are currently forthcoming. Further research in trial design to facilitate the estimation of the CATE is needed

Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces

Local higher-spin conserved currents are constructed in the supersymmetric sigma models with target manifolds symmetric spaces $G/H$. One class of currents is based on generators of the de Rham cohomology ring of $G/H$; a second class of currents are higher-spin generalizations of the (super)energy-momentum tensor. A comprehensive analysis of the invariant tensors required to construct these currents is given from two complimentary points of view, and sets of primitive currents are identified from which all others can be constructed as differential polynomials. The Poisson bracket algebra of the top component charges of the primitive currents is calculated. It is shown that one can choose the primitive currents so that the bosonic charges all Poisson-commute, while the fermionic charges obey an algebra which is a form of higher-spin generalization of supersymmetry. Brief comments are made on some implications for the quantized theories.Comment: 40 pages; LaTe

Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons

We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero modes in the fundamental representation from the ADHM construction. The number of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer index of the Dirac operator in the noncommutative instanton background. We point out that (super)conformal zero modes in non-BPS instantons are affected by the noncommutativity. The role of Lorentz symmetry breaking by the noncommutativity is also briefly discussed to figure out the structure of U(1) instantons.Comment: v3: 24 pages, Latex, corrected typos, references added, to appear in Phys. Rev.

ADHM Construction of Instantons on the Torus

We apply the ADHM instanton construction to SU(2) gauge theory on T^n x R^(4-n)for n=1,2,3,4. To do this we regard instantons on T^n x R^(4-n) as periodic (modulo gauge transformations) instantons on R^4. Since the R^4 topological charge of such instantons is infinite the ADHM algebra takes place on an infinite dimensional linear space. The ADHM matrix M is related to a Weyl operator (with a self-dual background) on the dual torus tilde T^n. We construct the Weyl operator corresponding to the one-instantons on T^n x R^(4-n). In order to derive the self-dual potential on T^n x R^(4-n) it is necessary to solve a specific Weyl equation. This is a variant of the Nahm transformation. In the case n=2 (i.e. T^2 x R^2) we essentially have an Aharonov Bohm problem on tilde T^2. In the one-instanton sector we find that the scale parameter, lambda, is bounded above, (lambda)^2 tv<4 pi, tv being the volume of the dual torus tilde T^2.Comment: 35 pages, LATeX. New section on Nahm transform included, presentation improved, reference added, to appear in Nuclear Physics