Global Spinors and Orientable Five-Branes

Fermion fields on an M-theory five-brane carry a representation of the double cover of the structure group of the normal bundle. It is shown that, on an arbitrary oriented Lorentzian six-manifold, there is always an Sp(2) twist that allows such spinors to be defined globally. The vanishing of the arising potential obstructions does not depend on spin structure in the bulk, nor does the six-manifold need to be spin or spin-C. Lifting the tangent bundle to such a generalised spin bundle requires picking a generalised spin structure in terms of certain elements in the integral and modulo-two cohomology of the five-brane world-volume in degrees four and five, respectively.Comment: 18 pages, LaTeX; v2: version to appear in JHE

Quantization of the Chern-Simons Coupling Constant

We investigate the quantum consistency of p-form Maxwell-Chern-Simons electrodynamics in 3p+2 spacetime dimensions (for p odd). These are the dimensions where the Chern--Simons term is cubic, i.e., of the form FFA. For the theory to be consistent at the quantum level in the presence of magnetic and electric sources, we find that the Chern--Simons coupling constant must be quantized. We compare our results with the bosonic sector of eleven dimensional supergravity and find that the Chern--Simons coupling constant in that case takes its corresponding minimal allowed value.Comment: 15 pages, 1 figure, JHEP3.cls. Equation (8.6) corrected and perfect agreement with previous results is obtaine

Twisted topological structures related to M-branes

Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tower of the orthogonal group, and demonstrate the relations to M-branes.Comment: 17 pages, title changed on referee's request, minor changes to improve presentation, typos correcte

The Exchange of Orientifold Two-Planes in M-theory

We propose an M-theory lift picture of the exchange among type IIA orientifold two-planes. This consists in wrapping a M5-brane on a three-cycle in the transverse space of the M-theory orientifold plane OM2. A flux quantization condition for the three-form self-dual field strength, on the worldvolume of the M5-brane is computed. This condition establishes the value which explains the relative charge between two different OM2-planes. Also, we find that the exchange of the four types of orientifold two-planes in string theory, has a common picture in M-theory. Moreover, we find that the assignment of the extra charge is fixed by cohomology and by the flux quantization of the field strength G in M-theory. We conclude that cohomology is sufficient to describe some orientifold properties in M-theory, that at string theory level, only K-theory is able to explain.Comment: 23+1 pages, 6 figures. v2: typos corrected, references adde

CFT/CFT interpolating RG flows and the holographic c-function

We consider holographic RG flows which interpolate between non-trivial ultra-violet (UV) and infra-red (IR) conformal fixed points. We study the ``superpotentials'' which characterize different flows and discuss their expansions near the fixed points. Then we focus on the holographic $c$-function as defined from the two-point function of the stress-energy tensor. We point out that the equation for the metric fluctuations in the background flow is equivalent to a scattering problem and we use this to obtain an expression for the $c$-function in terms of the associated Jost functions. We propose two explicit models that realize UV-IR flows. In the first example we consider a thin wall separating two AdS spaces with different radii, while in the second one the UV region is replaced with an asymptotically AdS space. We find that the holographic $c$-function obeys the expected properties. In particular it reduces to the correct -- nonzero -- central charge in the IR limit.Comment: 20 pages, discussion at the end of sec. 3 and sec. 4.1 change

Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincar\'e-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.Comment: 28 pages, plain Te

Superstring partition functions in the doubled formalism

Computation of superstring partition function for the non-linear sigma model on the product of a two-torus and its dual within the scope of the doubled formalism is presented. We verify that it reproduces the partition functions of the toroidally compactified type--IIA and type--IIB theories for appropriate choices of the GSO projection.Comment: 15 page

Universal Features of Holographic Anomalies

We study the mechanism by which gravitational actions reproduce the trace anomalies of the holographically related conformal field theories. Two universal features emerge: a) the ratios of type B trace anomalies in any even dimension are independent of the gravitational action, being uniquely determined by the underlying algebraic structure b) the normalization of the type A and the overall normalization of the type B anomalies are given by action dependent expressions with the dimension dependence completely fixed.Comment: 17 pages, harvma

On Exact Symmetries and Massless Vectors in Holographic Flows and other Flux Vacua

We analyze the isometries of Type IIB flux vacua based on the Papadopolous-Tseytlin ansatz and identify the related massless bulk vector fields. To this end we devise a general ansatz, valid in any flux compactification, for the fluctuations of the metric and p-forms that diagonalizes the coupled equations. We then illustrate the procedure in the simple case of holographic flows driven by the RR 3-form flux only. Specifically we study the fate of the isometries of the Maldacena-Nunez solution associated to wrapped D5-branes.Comment: 23 page

A Field-theoretical Interpretation of the Holographic Renormalization Group

A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we determine the relation between the holographic C theorem and the C theorem in two-dimensional quantum field theory which relies on the Zamolodchikov metric. Similarly we discuss how in four dimensions the holographic C function is related to a conjectured field-theoretical C function. The scheme dependence of the holographic RG due to the possible presence of finite local counterterms is discussed in detail, as well as its implications for the holographic C function. We also discuss issues special to the situation when mass deformations are present. Furthermore we suggest that the holographic RG equation may also be obtained from a bulk diffeomorphism which reduces to a Weyl transformation on the boundary.Comment: 24 pages, LaTeX, no figures; references added, typos corrected, paragraph added to section