Dimensional Supersymmetric Theories Research Articles

Dualities from Swampland principles

We initiate the program of bottom-up derivation of string theory dualities using Swampland principles. In particular, we clarify the relation between Swampland arguments and all the string theory dualities in d ≥ 9 dimensional supersymmetric theories. Our arguments center around the sharpened distance conjecture and rely on various other Swampland principles.

Chern–Simons theory in SIM(1) superspace

In this paper, we will analyse a three dimensional supersymmetric Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry, breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern-Simons theory with N=1 supersymmetry will break down to N=1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern-Simons action using SIM(1) projections of N=1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern-Simons action using these SIM(1) superfields. Furthermore, we will analyse the gauge symmetry of this Chern-Simons theory. This is the first time that a Chern-Simons theory with N=1/2 supersymmetry will be constructed on a manifold without a boundary.

Higher derivative terms in three dimensional supersymmetric theories

In this work, we systematically analyze higher derivative terms in the supersymmetric effective actions for three dimensional scalar field theories using $\mathcal{N} =1$ superspace formalism. In these effective actions, we show that auxiliary fields do not propagate and their effective actions can be expressed in terms of the physical fields. So, the theory does not change its field content upon addition of higher derivative terms. We use derivative expansion to generate four, five and six dimensional terms for an interacting scalar field theory with $\mathcal{N} =1$ supersymmetry. We show that along with pure fermionic and bosonic terms, there are various five and six dimensional topological terms that mix bosonic and fermionic fields. Finally, we use these results to obtain higher derivative topological terms in the effective action for two M2-branes.

Four dimensional supersymmetric theories in presence of a boundary

In this paper, we study N=1 supersymmetric theories in four dimensions in presence of a boundary. We demonstrate that it is possible to preserve half the supersymmetry of the original theory by suitably modifying it in presence of a boundary. This is done by adding new boundary terms to the original action, such that the supersymmetric variation of the new terms exactly cancels the boundary terms generated by the supersymmetric transformation of the original bulk action. We also analyze the boundary projections of such supercharges used in such a theory. We study super-Yang–Mills theories in presence of a boundary using these results. Finally, we study the Born–Infeld action in presence of a boundary. We analyze the boundary effects for the Born–Infeld action coupled to a background dilaton and an axion field. We also analyze the boundary effects for a non-abelian Born–Infeld action. We explicitly construct the actions for these systems in presence of a boundary. This action preserves half of the original supersymmetry.

On the low energy spectra of the non-supersymmetric heterotic string theories

The ten dimensional string theories as well as eleven dimensional supergravity are conjectured to arise as limits of a more basic theory, traditionally dubbed M-theory. This notion is confined to the ten dimensional supersymmetric theories. String theory, however, also contains ten dimensional non-supersymmetric theories that have not been incorporated into this picture. In this note we explore the possibility of generating the low energy spectra of various non-supersymmetric heterotic string vacua from the Horava–Witten model. We argue that this can be achieved by imposing on the Horava–Witten model an invariance with respect to some extra operators which identify the orbifold fixed planes in a non-trivial way, and we demonstrate it for the E8 and SO(16)×SO(16) heterotic string vacua in ten dimensions.

Phenomenological constraints on extra-dimensional scalars

We examine whether the ATLAS detector has sensitivity to extra-dimensional scalars (as opposed to components of higher-dimensional tensors which look like 4D scalars), in scenarios having the extra-dimensional Planck scale in the TeV range and n ⩾ 2 non-warped extra dimensions. Such scalars appear as partners of the graviton in virtually all higher dimensional supersymmetric theories. Using the scalar's lowest dimensional effective couplings to quarks and gluons, we compute the rate for the production of a hard jet together with missing energy. We find a non-trivial range of graviscalar couplings to which ATLAS could be sensitive, with experiments being more sensitive to couplings to gluons than to quarks. Graviscalar emission increases the missing-energy signal by adding to graviton production, and so complicates the inference of the extra-dimensional Planck scale from an observed rate. Because graviscalar differential cross-sections resemble those for gravitons, it is unlikely that these can be experimentally distinguished from one another should a missing-energy signal be observed.

Anomalously light mesons in a (1+1)-dimensional supersymmetric theory with fundamental matter

We consider N=1 supersymmetric Yang–Mills theory with fundamental matter in the large- N c approximation in 1+1 dimensions. We add a Chern–Simons term to give the adjoint partons a mass and solve for the meson bound states. Here mesons are color-singlet states with two partons in the fundamental representation but are not necessarily bosons. We find that this theory has anomalously light meson bound states at intermediate and strong coupling. We also examine the structure functions for these states and find that they prefer to have as many partons as possible at low longitudinal momentum fraction.

Dimensional Reduction over Coset Spaces and Supersymmetry Breaking

We address the question of supersymmetry breaking of a higher dimensional supersymmetric theory due to coset space dimensional reduction. In particular we study a ten-dimensional supersymmetric $E_{8}$ gauge theory which is reduced over all six-dimensional coset spaces. We find that the original supersymmetry is completely broken in the process of dimensional reduction when the coset spaces are symmetric. On the contrary softly broken four-dimensional supersymmetric theories result when the coset spaces are non-symmetric. From our analysis two promising cases are emerging which lead to interesting GUTs with three fermion families in four dimensions, one being non-supersymmetric and the other softly broken supersymmetric.

Hagedorn behaviour of little string theory from string corrections to NS5-branes

Following the conjectured duality between near-horizon NS5-branes and little string theory, the string-corrected thermodynamics of near-horizon NS5-branes is studied and found to agree with the statistical thermodynamics of a 5+1 dimensional supersymmetric string theory near the Hagedorn temperature. Specifically, tree-level corrections to the temperature are argued to vanish, in accordance with the duality, while the one-loop string correction to the NS5-brane thermodynamics is shown to generate the correct temperature dependence of the entropy.

On Four Dimensional Mirror Symmetry

A conjecture relating instanton calculus in four dimensional supersymmetric theories and the deformation theory of Lagrangian submanifolds in C2r invariant under a (subgroup of) Sp ( 2r, Z) is formulated. This is a four dimensional counterpart of the mirror symmetry of topological strings (relating Gromov-Witten invariants and generalized variations of Hodge structure).

D = (0|2) DIRAC–MAXWELL–EINSTEIN THEORY AS A WAY FOR DESCRIBING SUPERSYMMETRIC QUARTIONS

Drawing an analogy with the Dirac theory of fermions interacting with electromagnetic and gravitational field we write down supersymmetric equations of motion and construct a superfield action for particles with spin [Formula: see text] and [Formula: see text] (quartions), where the role of quartion momentum in effective (2+1)-dimensional space–time is played by an Abelian gauge superfield propagating in a basic two-dimensional Grassmann-odd space with a cosmological constant showing itself as the quartion mass. So, the (0|2) (0 even and 2 odd) dimensional model of quartions interacting with the gauge and gravitational field manifests itself as an effective (2 + 1)-dimensional supersymmetric theory.

STrM2 SUM RULE FOR A GENERAL CLASS OF KÄHLER POTENTIALS

We study the sum rule for the mass squared of the N = 1 four dimensional effective supersymmetric theory whose Kähler potential is of the general form that appears in compactified superstrings. We take full account of the non-minimal nature of the models. We discuss the conditions under which one can have both a vanishing cosmological constant and a zero STr M2.

Chiral anomalies in higher dimensional supersymmetric theories

We derive explicit formulas for pure gauge anomalies in a SYM theory in 6D as well as in 10D. Each anomaly consists of two terms: a gauge cocycle and a cocycle of the superdiffeomorphisms. The derivation is based essentially on a remarkable property of supersymmetric theories which we call Weil triviality and is directly connected with the constraints. The analogous problem for Lorentz anomalies is stated in the same way. However, in general, there are difficulties concerning Weil triviality. We prove that for pure SUGRA in 6D as well as in 10D it is possible to prove Weil triviality and, consequently, to obtain explicit expressions for pure Lorentz anomalies. However, as far as SUGRA coupled to SYM à la Chapline-Manton or à la Green-Schwarz is concerned, no self-evident solution is available.

Boundary effects on the soliton mass in (1+1)-dimensional supersymmetric theories

A proper incorporation of boundary effects, in terms of a surface term contribution to the one-loop soliton mass in (1+1)-dimensional supersymmetric theories, is shown to resolve the problem of renormalizability in the soliton sector, which otherwise arises in a finite space calculation of the soliton mass using a modified version of a set of boundary conditions proposed by Rouhani. The saturation of the Witten-Olive bound for such boundary conditions follows immediately.

Soliton mass distributions in (1+1)-dimensional supersymmetric theories

The renormalized mass distribution is evaluated to one-loop order for solutions in (1+1)-dimensional supersymmetric theories. The Witten-Olive equality for the mass and the central charge is found to hold already for the respective densities. We also find that there is no correction to the total mass for the supersymmetric (sinϕ) 2 theory at this order, although the correction to the mass distribution is nonvanishing.