Jumps and twists in affine Toda field theories

The concept of point-like “jump” defects is investigated in the context of affine Toda field theories. The Hamiltonian formulation is employed for the analysis of the problem. The issue is also addressed when integrable boundary conditions ruled by the classical twisted Yangian are present. In both periodic and boundary cases explicit expressions of conserved quantities as well as the relevant Lax pairs and sewing conditions are extracted. It is also observed that in the case of the twisted Yangian the bulk behavior is not affected by the presence of the boundaries

Classical impurities associated to high rank algebras

Classical integrable impurities associated with high rank ( <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi mathvariant="fraktur">gl</mi></mrow><mrow><mi>N</mi></mrow></msub></math> ) algebras are investigated. A particular prototype, i.e. the vector non-linear Schrödinger (NLS) model, is chosen as an example. A systematic construction of local integrals of motion as well as the time components of the corresponding Lax pairs is presented based on the underlying classical algebra. Suitable gluing conditions compatible with integrability are also extracted. The defect contribution is also examined in the case where non-trivial integrable conditions are implemented. It turns out that the integrable boundaries may drastically alter the bulk behavior, and in particular the defect contribution

Bose condensation and branes

When the cosmological constant is considered to be a thermodynamical variable in black hole thermodynamics, analogous to a pressure, its conjugate variable can be thought of as a thermodynamic volume for the black hole. In the AdS/CFT correspondence this interpretation cannot be applied to the CFT on the boundary but, from the point of view of the boundary SU( N ) gauge theory, varying the cosmological constant in the bulk is equivalent to varying the number of colors in the gauge theory. This interpretation is examined in the case of AdS 5 × S 5 , for N = 4 $$\mathcal{N}=4$$ SUSY Yang-Mills at large N , and the variable thermodynamically conjugate to N , a chemical potential for color, is determined. It is shown that the chemical potential in the high temperature phase of the Yang-Mills theory is negative and decreases as temperature increases, as expected. For spherical black holes in the bulk the chemical potential approaches zero as the temperature is lowered below the Hawking-Page temperature and changes sign at a temperature that is within one part in a thousand of the temperature at which the heat capacity diverges

Dirac operators on the Taub-NUT space, monopoles and SU(2) representations

We analyse the normalisable zero-modes of the Dirac operator on the TaubNUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to a Dirac monopole. We show that the space of zero modes decomposes into a direct sum of irreducible SU(2) representations of all dimensions up to a bound determined by the spinor charge with respect to the abelian gauge group. Our decomposition provides an interpretation of an index formula due to Pope and provides a possible model for spin in recently proposed geometric models of matter

Harmonic forms on ALF gravitational instantons

We study the space of square-integrable harmonic forms over ALF gravitational instantons of type A K −1 and of type D K . We first calculate its dimension making use of a result by Hausel, Hunsicker and Mazzeo which relates the Hodge cohomology of a gravitational instanton M to the singular cohomology of a particular compactification X M of M . We then exhibit an explicit basis, exact for A K −1 and approximate for D K , and interpret geometrically the relations between M , X M and their cohomologies

Bootstrapping fuzzy scalar field theory

We describe a new way of rewriting the partition function of scalar field theory on fuzzy complex projective spaces as a solvable multitrace matrix model. This model is given as a perturbative high-temperature expansion. At each order, we present an explicit analytic expression for most of the arising terms; the remaining terms are computed explicitly up to fourth order. The method presented here can be applied to any model of hermitian matrices. Our results confirm constraints previously derived for the multitrace matrix model by Polychronakos. A further implicit expectation about the shape of the multitrace terms is however shown not to be true

Lie 2-algebra models

In this paper, we begin the study of zero-dimensional field theories with fields taking values in a semistrict Lie 2-algebra. These theories contain the IKKT matrix model and various M-brane related models as special cases. They feature solutions that can be interpreted as quantized 2-plectic manifolds. In particular, we find solutions corresponding to quantizations of $\mathbb{R}$ 3 , S 3 and a five-dimensional Hpp-wave. Moreover, by expanding a certain class of Lie 2-algebra models around the solution corresponding to quantized $\mathbb{R}$ 3 , we obtain higher BF-theory on this quantized space

Semistrict higher gauge theory

We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Čech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due to Ševera. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non-Abelian N = 2 0 $$\mathcal{N}=\left(2,0\right)$$ tensor multiplet taking values in a semistrict Lie 2-algebra

On the groundstate of octonionic matrix models in a ball

In this work we examine the existence and uniqueness of the groundstate of a SU(N)×G2 octonionic matrix model on a bounded domain of RN . The existence and uniqueness argument of the groundstate wavefunction follows from the Lax–Milgram theorem. Uniqueness is shown by means of an explicit argument which is drafted in some detail

Sasakian quiver gauge theories and instantons on cones over lens 5-spaces

We consider SU(3) -equivariant dimensional reduction of Yang–Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki–Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki–Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3) -equivariant solutions to the Hermitian Yang–Mills equations on the associated Calabi–Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as Kähler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces