Dimensional Supersymmetric Yang-Mills Theory Research Articles

The Dirac–Higgs Complex and Categorification of (BBB)-Branes

Abstract Let ${\mathcal{M}}_{\operatorname{Dol}}(X,G)$ denote the hyperkähler moduli space of $G$-Higgs bundles over a smooth projective curve $X$. In the context of four dimensional supersymmetric Yang–Mills theory, Kapustin and Witten introduced the notion of (BBB)-brane: boundary conditions that are compatible with the B-model twist in every complex structure of ${\mathcal{M}}_{\operatorname{Dol}}(X,G)$. The geometry of such branes was initially proposed to be hyperkähler submanifolds that support a hyperholomorphic bundle. Gaiotto has suggested a more general type of (BBB)-brane defined by perfect analytic complexes on the Deligne–Hitchin twistor space $\operatorname{Tw}({\mathcal{M}}_{\operatorname{Dol}}(X,G))$. Following Gaiotto’s suggestion, this paper proposes a framework for the categorification of (BBB)-branes, both on the moduli spaces and on the corresponding derived moduli stacks. We do so by introducing the Deligne stack, a derived analytic stack with corresponding moduli space $\operatorname{Tw}({\mathcal{M}}_{\operatorname{Dol}}(X,G))$, defined as a gluing between two analytic Hodge stacks along the Riemann–Hilbert correspondence. We then construct a class of (BBB)-branes using integral functors that arise from higher non-abelian Hodge theory, before discussing their relation to the Wilson functors from the Dolbeault geometric Langlands correspondence.

Superfield description of [formula omitted]-dimensional SYM theories and their mixtures on magnetized tori

We provide a systematic way of dimensional reduction for (4+2n)-dimensional U(N) supersymmetric Yang–Mills (SYM) theories (n=0,1,2,3) and their mixtures compactified on two-dimensional tori with background magnetic fluxes, which preserve a partial N=1 supersymmetry out of full N=2,3 or 4 in the original SYM theories. It is formulated in an N=1 superspace respecting the unbroken supersymmetry, and the four-dimensional effective action is written in terms of superfields representing N=1 vector and chiral multiplets, those arise from the higher-dimensional SYM theories. We also identify the dilaton and geometric moduli dependence of matter Kähler metrics and superpotential couplings as well as of gauge kinetic functions in the effective action. The results would be useful for various phenomenological/cosmological model buildings with SYM theories or D-branes wrapping magnetized tori, especially, with mixture configurations of them with different dimensionalities from each other.

Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory

In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.

Supersymmetric duality in superloop space

In this paper we constructed superloop space duality for a four dimensional supersymmetric Yang–Mills theory with \(\mathcal {N} =1\) supersymmetry. This duality reduces to the ordinary loop space duality for the ordinary Yang–Mills theory. It also reduces to the Hodge duality for an abelian gauge theory. Furthermore, the electric charges, which are the sources in the original theory, appear as monopoles in the dual theory. Whereas, the magnetic charges, which appear as monopoles in the original theory, become sources in the dual theory.

Supersymmetric Duality in Deformed Superloop Space

In this paper, we will analyse the superloop space formalism for a four dimensional supersymmetric Yang–Mills theory in deformed superspace. We will deform the \(\mathcal {N} =1\) superspace by imposing imposing non-anticommutativity. This non-anticommutative deformation of the superspace will break half the supersymmetry of the original theory. So, this theory will have \(\mathcal {N} =1/2\) supersymmetry. We will analyse the superloop space duality for this deformed supersymmetric Yang–Mills theory using the \(\mathcal {N} =1/2\) superspace formalism. We will demonstrate that the sources in the original theory will become monopoles in the dual theory, and the monopoles in the original theory will become sources in the dual theory.

Super-Yang-Mills theory inSIM(1)superspace

In this paper, we will analyse three dimensional supersymmetric Yang-Mills theory coupled to matter fields in $SIM(1)$ superspace formalism. The original theory which is invariant under the full Lorentz group has $\mathcal{N} =1$ supersymmetry. However, when we break the Lorentz symmetry down to $SIM(1)$ group, the $SIM(1)$ superspace will break half the supersymmetry of the original theory. Thus, the resultant theory in $SIM(1)$ superspace will have $\mathcal{N} =1/2$ supersymmetry. This is the first time that $\mathcal{N} =1 $ supersymmetry will be broken down to $\mathcal{N} =1/2$ supersymmetry, for a three dimensional theory, on a manifold without a boundary. This is because it is not possible to use non-anticommutativity to break $\mathcal{N} =1$ supersymmetry down to $\mathcal{N} =1/2$ supersymmetry in three dimensions.

Black-hole–black-string phase transitions in thermal (1 + 1)-dimensional supersymmetric Yang–Mills theory on a circle

We review and extend earlier work that uses the AdS/CFT correspondence to relate the black-hole–black-string transition of gravitational theories on a circle to a phase transition in maximally supersymmetric (1 + 1)-dimensional SU(N) gauge theories at large N, again compactified on a circle. We perform gravity calculations to determine a likely phase diagram for the strongly coupled gauge theory. We then directly study the phase structure of the same gauge theory, now at weak 't Hooft coupling. In the interesting temperature regime for the phase transition, the (1 + 1)-dimensional theory reduces to a (0 + 1)-dimensional bosonic theory, which we solve using Monte Carlo methods. We find strong evidence that the weakly coupled gauge theory also exhibits a black hole–black string-like phase transition in the large N limit. We demonstrate that a simple Landau–Ginzburg-like model describes the behaviour near the phase transition remarkably well. The weak coupling transition appears to be close to the cusp between a first-order and a second-order transition.

D1/D5 system and Wilson loops in (non)commutative gauge theories

We study the behavior of the Wilson loop in the (5+1)-dimensional supersymmetric Yang–Mills theory with the presence of the solitonic object. Using the dual string description of the Yang–Mills theory that is given by the D1/D5 system, we estimate the Wilson loops both in the temporal and spatial cases. For the case of the temporal loop, we obtain the velocity dependent potential. For the spatial loop, we find that the area law is emerged due to the effect of the D1-branes. Further, we consider D1/D5 system in the presence of the constant B field. It is found that the Wilson loop obeys the area law for the effect of the noncommutativity.

Effective action for membrane dynamics in DLCQ M theory on a two-torus

The effective action for the membrane dynamics on the background geometry of the $N$-sector DLCQ $M$ theory compactified on a two-torus is computed via supergravity. We compare it to the effective action obtained from the matrix theory, i.e., the (2+1)-dimensional supersymmetric Yang-Mills (SYM) theory, including the one-loop perturbative and full non-perturbative instanton effects. Consistent with the DLCQ prescription of $M$ theory {\em a la} Susskind, we find the precise agreement for the finite $N$-sector (off-conformal regime), as well as for the large $N$ limit (conformal regime), providing us with a concrete example of the correspondence between the matrix theory and the DLCQ $M$ theory. Non-perturbative instanton effects in the SYM theory conspire to yield the eleven-dimensionally covariant effective action.

SO(9, 1) invariant matrix formulation of a supermembrane

An $SO(9,1)$ invariant formulation of an 11-dimensional supermembrane is presented by combining an $SO(10,1)$ invariant treatment of reparametrization symmetry with an $SO(9,1)$ invariant $\theta_{R} = 0$ gauge of $\kappa$-symmetry. The Lagrangian thus defined consists of polynomials in dynamical variables (up to quartic terms in $X^{\mu}$ and up to the eighth power in $\theta$), and reparametrization BRST symmetry is manifest. The area preserving diffeomorphism is consistently incorporated and the area preserving gauge symmetry is made explicit. The $SO(9,1)$ invariant theory contains terms which cannot be induced by a naive dimensional reduction of higher dimensional supersymmetric Yang-Mills theory. The $SO(9,1)$ invariant Hamiltonian and the generator of area preserving diffeomorphism together with the supercharge are matrix regularized by applying the standard procedure. As an application of the present formulation, we evaluate the possible central charges in superalgebra both in path integral and in canonical (Dirac) formalism, and we find only the two-form charge $[X^\mu, X^\nu]$.

Schwarzschild Black Holes from Matrix Theory

We consider matrix theory compactified on T{sup 3} and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the mass-entropy relation, the Hawking temperature, and the physical size, up to numerical factors of order unity. The most economical description involves setting the cutoff N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional supersymmetric Yang-Mills theory with 16supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski. {copyright} {ital 1998} {ital The American Physical Society}

Special Quantum Field Theories¶in Eight and Other Dimensions

We build nearly topological quantum field theories in various dimensions. We give special attention to the case of 8 dimensions for which we first consider theories depending only on Yang-Mills fields. Two classes of gauge functions exist which correspond to the choices of two different holonomy groups in SO(8), namely SU(4) and Spin(7). The choice of SU(4) gives a quantum field theory for a Calabi-Yau fourfold. The expectation values for the observables are formally holomorphic Donaldson invariants. The choice of Spin(7) defines another eight dimensional theory for a Joyce manifold which could be of relevance in M- and F-theories. Relations to the eight dimensional supersymmetric Yang-Mills theory are presented. Then, by dimensional reduction, we obtain other theories, in particular a four dimensional one whose gauge conditions are identical to the non-abelian Seiberg-Witten equations. The latter are thus related to pure Yang-Mills self-duality equations in 8 dimensions as well as to the N=1, D=10 super Yang-Mills theory. We also exhibit a theory that couples 3-form gauge fields to the second Chern class in eight dimensions, and interesting theories in other dimensions.

Matrices on a point as the theory of everything

It is shown that the world line can be eliminated in the matrix quantum mechanics conjectured by Banks, Fischler, Shenker, and Susskind to describe the light-cone physics of M theory. The resulting matrix model has a form that suggests origins in the reduction to a point of a Yang-Mills theory. The reduction of the Nishino-Sezgin (10+2)-dimensional supersymmetric Yang-Mills theory to a point gives a matrix model with the appropriate features: Lorentz invariance in $9+1$ dimensions, supersymmetry, and the correct number of physical degrees of freedom.

D-PARTICLE DYNAMICS AND BOUND STATES

We study the low energy effective theory describing the dynamics of D-particles. This corresponds to the quantum-mechanical system obtained by dimensional reduction of (9+1)-dimensional supersymmetric Yang-Mills theory to 0+1 dimensions and can be interpreted as the nonrelativistic limit of the Born-Infeld action. We study the system of two like-charged D-particles and find evidence for the existence of non-BPS states whose mass grows like λ1/3 over the BPS mass. We give a string interpretation of this phenomenon in terms of a linear potential generated by strings stretching from the two D-particles. Some comments on the possible relations to black hole entropy and elevendimensional supergravity are also given.

Quenched two dimensional supersymmetric Yang-Mills theory

By studying the pure Yang-Mills theory on a circle, as well as an adjoint scalar coupled to the gauge field on a circle, we propose a quenching prescription in which the combination of the spatial component of the gauge field and P is treated as a dynamic variable. Averaging over momentum is not necessary, therefore the usual ultraviolet cut-off is eliminated. We then apply this prescription to study the large N two dimensional supersymmetric gauge theory. An one dimensional supersymmetric matrix model is obtained. It is not known whether this model can be solved exactly. However, an extended model with one more complex fermion is exactly solvable, with N = 1 supersymmetry as Parisi-Sourlas supersymmetry. The exact solvability may have some implications for the N = 1 quenched model.

Ultraviolet divergences in higher dimensional supersymmetric Yang-Mills theories

We determine the loop orders for the onset of allowed ultra-violet divergences in higher dimensional supersymmetric Yang-Mills theories. Cancellations are controlled by the non-renormalization theorems for the linearly realizable supersymmetries and by the requirement that counterterms display the full non-linear supersymmetries when the classical equations of motion are imposed. The first allowed divergences in the maximal super Yang-Mills theories occur at four loops in five dimensions, three loops in six dimensions and two loops in seven dimensions.