Supersymmetric Charges Research Articles

Supersymmetric charge constraints on AdS black holes from free fields

Supersymmetric AdS black hole solutions exist only when their angular momenta and charges satisfy a certain constraint that depends on the dimension. We show that these nonlinear relations on the conserved charges agree with a computation in the dual supersymmetric CFT in its free limit, with interactions entering only through a uniform rescaling of all charges. Our computations apply to the highly non-trivial charge constraints for AdS4, AdS5 and AdS7 black holes, and generalize an earlier one for the analogous constraint in AdS3. Our results suggest a microscopic understanding of AdS black holes beyond the scope of supersymmetric indices.

On the ℤ2 topological invariant

We develop a complex fermionic field-based method to model the properties of the filled bands of topological two-dimensional (2D) matter with time reversal (TR)-symmetry. Using this fermionic representation, we give an explicit calculation of the [Formula: see text] index for 2D topological matter invariant under TR and comment on the emergence of Majorana states at the TR-fix points. Moreover, motivated by recent theoretical results on possible signatures of topological supersymmetric matter, we also give the supersymmetric generalization of our TR-invariant construction and calculate the underlying topological [Formula: see text] index. Other features such as the topological obstruction of basis sections in the fermionic determinant bundle are also investigated. Applications for the calculations of the supersymmetric charge [Formula: see text] operator and the super-Hamiltonian [Formula: see text] for the three-dimensional topological class AII are undertaken; these operators are given by Eqs. (5.48)–(5.51).

Magnetic charges in supergravity

In this paper we study the dual charges of mathcal{N} = 1 supergravity in asymptotically flat space-time. The action considered is the usual supergravity action with a topological contribution. This is the Nieh-Yan term and the magnetic term of the free Rarita-Schwinger field. Through methods of the covariant phase space formalism we construct the charges conjugate to supersymmetry, diffeomorphism and Lorentz transformations. The additional term in the action will lead to new, non-vanishing contributions to these charges. The magnetic diffeomorphism charges are equivalent to the ones previously found for gravity, while the dual supersymmetric charges are new and do not appear for the free Rarita-Schwinger field. The dual Lorentz charges serve to regularize the previous two. We find that the asymptotic symmetry group for supergravity can only include globally well-defined super-rotations.

Supercharge optical arrays.

We introduce the notion of a supercharge optical array synthesized according to supersymmetric charge operators. Starting from an arbitrary array, mathematical supersymmetry transformation can be used systematically to create a zero-energy physical state below the ground state of the super-partner array. This zero mode, which is pinned deep in the mid-gap of the corresponding supercharge array owing to the square-root spectral relationship between a supercharge and a super-Hamiltonian array, is shown to be protected because of the chiral symmetry inherent to a supercharge array. A supercharge array can be used in practical applications to design a discrete optical system of waveguides or coupled resonators where the mid-gap zero mode facilitates robust light dynamics in either spatial or time domain.

The Ground State of the D = 11 Supermembrane: the External Dirichlet Problem

We analyse the outer Dirichlet problem for the Hamiltonian of the SU(N) regularized D = 11 Supermembrane. We show the existence and uniqueness of the solution for this problem. The solution belongs to a suitable Hilbert space, introduced in the present work, which is defined in terms of the supersymmetric charges. The existence and uniqueness of the ground state of the D = 11 supermembrane is directly related to the patching of solutions of the inner and outer Dirichlet problems.

The ground state of the D = 11 supermembrane and matrix models on compact regions

We establish a general framework for the analysis of boundary value problems of matrix models at zero energy on compact regions. We derive existence and uniqueness of ground state wavefunctions for the mass operator of the D=11 regularized supermembrane theory, that is the N=16 supersymmetric SU(N) matrix model, on balls of finite radius. Our results rely on the structure of the associated Dirichlet form and a factorization in terms of the supersymmetric charges. They also rely on the polynomial structure of the potential and various other supersymmetric properties of the system.

Quantum theories of (p, q)-forms

We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge invariances. The latter can be seen as building blocks of the former. Their equations of motion can be obtained in a natural way by first-quantizing a spinning particle with a U(2)-extended supersymmetry on the worldline. The particle system contains four supersymmetric charges, represented quantum mechanically by the Dolbeault operators and their hermitian conjugates. After studying how the (p,q)-form field theories emerge from the particle system, we investigate their one loop effective actions, identify corresponding heat kernel coefficients, and derive exact duality relations. The dualities are seen to include mismatches related to topological indices and analytic torsions, which are computed as Tr(-1)^F and Tr[(-1)^F F] in the first quantized supersymmetric nonlinear sigma model for a suitable fermion number operator F.

SUPERSYMMETRIC YANG–MILLS THEORIES WITH EXACT SUPERSYMMETRY ON THE LATTICE

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang–Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean space–time lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice [Formula: see text] SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.

On the supersymmetric vacua of the Veneziano–Wosiek model

We study the supersymmetric vacua of the Veneziano-Wosiek model in sectors with fermion number F=2, 4 at finite 't Hooft coupling lambda. We prove that for F=2 there are two zero energy vacua for lambda > lambda_c = 1 and none otherwise. We give the analytical expressions of both vacua. One of them was previously known, the second one is obtained by solving the cohomology of the supersymmetric charges. At F=4 we compute the would-be supersymmetric vacua at high order in the the strong coupling expansion and provide strong support to the conclusion that lambda = 1 is a critical point in this sector too. It separates a strong coupling phase with two symmetric vacua from a weak coupling phase with positive spectrum.

SUPERSYMMETRIC WZW σ MODEL ON INFINITE AND HALF-PLANE

We study classical integrability of the supersymmetric U(N) σ model with the Wess–Zumino–Witten term on infinite and half-plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit forms of the first few supersymmetric charges are constructed. We show that the considered model is integrable on infinite plane as a consequence of the conservation of the supersymmetric charges. Also, we study the model on half-plane with free boundary, and examine the conservation of the supersymmetric charges on half-plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half-plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.

Exact Witten index in D=2 supersymmetric Yang–Mills quantum mechanics

A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang–Mills quantum mechanics in any dimensions. For the D=2 system with the SU(2) gauge group, considered here, the technique gives exact, closed expressions for arbitrary matrix elements of the hamiltonian and of the supersymmetric charge, in the occupation number representation. Subsequent numerical diagonalization provides spectrum and restricted Witten index of the system with very high precision (taking into account up to 105 quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time.

New vortex solution inSU(3)gauge-Higgs theory

Following a brief review of known vortex solutions in SU(N) gauge-adjoint Higgs theories we show the existence of a new ``minimal'' vortex solution in SU(3) gauge theory with two adjoint Higgs bosons. At a critical coupling the vortex decouples into two abelian vortices, satisfying Bogomol'nyi type, first order, field equations. The exact value of the vortex energy (per unit length) is found in terms of the topological charge that equals to the N=2 supersymmetric charge, at the critical coupling. The critical coupling signals the increase of the underlying supersymmetry.

Large N limit of extremal non-supersymmetric black holes

The large N limit of extremal non-supersymmetric Type-I five-dimensional string black holes is studied from the point of view of D-branes. We find that the agreement between the D-brane and the black-hole picture is due to an asymptotic restoration of supersymmetry in the large N limit in which both pictures are compared. In that limit Type-I string perturbation theory is effectively embedded into a Type-IIB perturbation theory with unbroken supersymmetric charges whose presence guarantees the non-renormalization of mass and entropy as the effective couplings are increased. In this vein, we also study the near-horizon geometry of the Type-I black hole using D5-brane probes to find that the low-energy effective action for the probe is identical to the corresponding one in the auxiliary Type-IIB theory in the large N limit.

Scattering of four-dimensional black holes

The moduli space metric for an arbitrary number of extremal black holes in four dimensions with arbitrary relatively supersymmetric charges is found.

Scattering of several multiply charged extremal D = 5 black holes

The moduli space metric for an arbitrary number of extremal D = 5 black holes with arbitrary relatively supersymmetric charges is found.

Scattering potentials with LS-terms from first-order Casimir operators

Using a first-order Casimir operator calculated in a non-standard realization for the so(3,1) algebra, we obtain a one-dimensional scattering problem with LS-type interaction terms. It is shown that for this realization the square of this operator can be expressed in terms of the usual quadratic Casimir. Due to this constraint the scattering states are completely specified by restricting the possible set of eigenvalues accordingly. The results show that the use of extra Casimir operators can provide additional insight into the group theoretical structure of the scattering problem. A generalization for the so(2n-1,1), n>2 case is also given. The underlying supersymmetry of the resulting Schrodinger equations is pointed out. The supersymmetric charge operators are related to our first-order Casimir operators.

Supersymmetric quantum mechanics, anomalies and factorization

The explicit symmetry breaking phenomenon in supersymmetric quantum mechanics (SUSY QM) is analysed in terms of anomalies. The anomalous behaviour can be assigned to the supersymmetric charges which define the two Hamiltonians of the model. The relation between the presence of anomalies and the factorization of the Schrodinger equations is also discussed.

Relationship between supersymmetry and solvable potentials.

We investigate whether a general class of solvable potentials, the Natanzon potentials (those potentials whose solutions are hypergeometric functions), and their supersymmetric partner potentials are related by a discrete reparametrization invariance called ``shape invariance'' discovered by Genden- shtein. We present evidence that this is not the case in general. Instead we find that the Natanzon class of potentials is not the most general class of solvable potentials but instead belongs to a wider class of potentials generated by supersymmetry and factorization whose eigenfunctions are sums of hypergeometric functions. The series of Hamiltonians, together with the corresponding supersymmetric charges form the graded Lie algebra sl(1/1)\ensuremath{\bigotimes}SU(2). We also present a strategy for solving, in a limited domain, the discrete reparametrization invariance equations connected with ``shape invariance.''

Non-existence of renormalizable self-interaction in N = 2 supersymmetry for scalar hypermultiplets

We prove that the assumption of invariance under “isospin rotations”, i.e. automorphisms of N = 2 supersymmetric charges, implies that there is no local renormalizable interaction among scalar hypermultiplets.

A remark on spontaneous breaking of supersymmetry

The anticommutation relations of supersymmetric charges are discussed in the case of spontaneous breaking.