We construct a pseudoclassical particle model associated to the twisted N=2 SUSY algebra in four dimensions. The particle model has four kappa symmetries. Three of them can be used to reduce the model to the vector supersymmetry particle case. The quantization of the model gives rise to two copies of the 4d Dirac equation. The kappa symmetries result to be associated to 4 TSUSY invariant bilinear odd operators who are null operators when a particular condition is satisfied. These operators are in correspondence one to one with analogous operators existing in the case of the N=2 SUSY algebra, making both cases 1/2 BPS.
We present SuperMaxwell algebra: an N=1, D=4 algebra with two Majorana supercharges, obtained as the minimal enlargement of superPoincare containing the Maxwell algebra as a subalgebra. The new superalgebra describes the supersymmetries of generalized N=1, D=4 superspace in the presence of a constant Abelian SUSY field strength background. Applying the techniques of non-linear coset realization to the Maxwell supergroup we propose a new kappa-invariant massless superparticle model providing a dynamical realization of the SuperMaxwell algebra.
A generalization of the twistor shift procedure to the case of superparticle interacting with the background D=3 N=1 Maxwell and D=3 N=1 supergravity supermultiplet is considered. We investigate twistor shift effects and discuss the structure of the resulting constraint algebra.
We discuss a deformation of superspace based on a hermitian twist. The twist implies a $\star$-product that is noncommutative, hermitian and finite when expanded in power series of the deformation parameter. The Leibniz rule for the twisted SUSY transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model…
We propose N=4 twisted superspace formalism in four dimensions by introducing Dirac-Kahler twist. In addition to the BRST charge as a scalar counter part of twisted supercharge we find vector and tensor twisted supercharges. By introducing twisted chiral superfield we explicitly construct off-shell twisted N=4 SUSY invariant action. We can propose variety of supergauge invariant actions by introducing twisted vector superfield. We may, however, need to find further constraints to identify twisted N=4 super Yang-Mills action. We propose a superconnection formalism of twisted superspace where co…
A global supersymmetry (SUSY) in supersymmetric gauge theory is generally broken by gauge fixing. A prescription to extract physical information from such SUSY algebra broken by gauge fixing is analyzed in path integral framework. If $δ_{SUSY}δ_{BRST}Ψ= δ_{BRST}δ_{SUSY}Ψ$ for a gauge fixing ``fermion'' $Ψ$, the SUSY charge density is written as a sum of the piece which is naively expected without gauge fixing and a BRST exact piece. If $δ_{SUSY}δ_{SUSY}δ_{BRST}Ψ= δ_{BRST}δ_{SUSY}δ_{SUSY}Ψ$, the equal-time anti-commutator of SUSY charge is written as a sum of a physical piece and a BRST exact p…
We reinvestigate the twisted N=4 supersymmetry present in Schwarz type topological field models. We show that Chern-Simons theory in three dimensions can be untwisted to a kind of sigma-model with reversed statistics only in the free case. By dimensional reduction we define then the two-dimensional BF-model. We establish an analog result concerning the untwisting. As a consequence of the definition through dimensional reduction we find new fermionic scalar symmetries that have been overlooked so far in the literature.
We calculate partition function and correlation functions in A-twisted 2d $\mathcal{N}=(2,2)$ theories and topologically twisted 3d $\mathcal{N}=2$ theories containing adjoint chiral multiplet with particular choices of $R$-charges and the magnetic fluxes for flavor symmetries. According to Gauge-Bethe correspondence, they correspond to Heisenberg XXX and XXZ spin chain models. We identify the partition function as the inverse of the norm of the Bethe eigenstates. Correlation functions are identified as the coefficients of the expectation value of Baxter $Q$-operators. In addition, we consider…
Predictions for the scale of SUSY breaking from the string landscape go back at least a decade to the work of Denef and Douglas on the statistics of flux vacua. The assumption that an assortment of SUSY breaking F and D terms are present in the hidden sector, and their values are uniformly distributed in the landscape of D=4, N=1 effective supergravity models, leads to the expectation that the landscape pulls towards large values of soft terms favored by a power law behavior P(m(soft))~ m(soft)^n. On the other hand, similar to Weinberg's prediction of the cosmological constant, one can assume …
Non-anticommutative deformations have been studied in the context of supersymmetry (SUSY) in three and four space-time dimensions, and the general picture is that highly nontrivial to deform supersymmetry in a way that still preserves some of its important properties, both at the formal algebraic level (e.g., preserving the associativity of the deformed theory) as well as at the physical level (e.g., maintaining renormalizability). The Hopf algebra formalism allows the definition of algebraically consistent deformations of SUSY, but this algebraic consistency does not guarantee that physical m…
We propose a twisted SUSY invariant formulation of Chern-Simons theory on a Euclidean three dimensional lattice. The SUSY algebra to be realized on the lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et al.. In order to keep the manifest anti-hermiticity of the action, we introduce oppositely oriented supercharges. Accordingly, the naive continuum limit of the action formally corresponds to the Landau gauge fixed version of Chern-Simons theory with complex gauge group which was originally proposed by Witten. We also show that the resulting action consists of parity …
$\mathcal{N}=1$ SUSY Yang-Mills theory is an appealing theoretical framework that has been studied in the literature using different methods, including standard lattice simulations. Among these, the volume-reduced twisted Eguchi-Kawai model, endowed with one adjoint Majorana fermion, could play an important role in studying its large-$N$ limit via the Curci-Veneziano prescription. In this talk, we present our results on the analysis of the scale of the theory, performed via different methods based on purely gluonic observables as well as (quenched) fundamental mesons in the chiral limit. These…
In this paper, using a Hopf-algebraic method, we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincaré algrebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for N=1 case. We also comment on the possibility of noncommutative central …
Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a…
The quantum SUSY N=1 hierarchy based on $sl(2|1)^{(2)}$ twisted affine superalgebra is considered. The construction of the corresponding Baxter's Q-operators and fusion relations is outlined. The relation with the superconformal field theory is discussed.
We study instanton contributions to the superpotential of local F-theory compactifications which could potentially be used to engineer models of dynamical supersymmetry breaking. These instantons correspond to Euclidean 3-branes which form a threshold bound state with spacetime filling 7-branes. In certain cases, their contributions to the effective 4d superpotential can be determined in both perturbative string theory as well as directly via the topologically twisted theory on the 3-brane worldvolume, and in all cases we observe an exact match between these results. We further present an inst…
We study examples of chiral four-dimensional IIB orientifolds with Scherk--Schwarz supersymmetry breaking, based on freely acting orbifolds. We construct a new Z3xZ3' model, containing only D9-branes, and rederive from a more geometric perspective the known Z6'xZ2' model, containing D9, D5 and \bar D 5 branes. The cancellation of anomalies in these models is then studied locally in the internal space. These are found to cancel through an interesting generalization of the Green--Schwarz mechanism involving twisted Ramond--Ramond axions and 4-forms. The effect of the latter amounts to local coun…
We construct the consistent supersymmetric extensions of the operators describing the recoil of a D-brane and show that they realize an N=1 logarithmic superconformal algebra. The corresponding supersymmetric vertex operator is related to the action of a twisted superparticle with twist field determined by the angular momentum of the recoiling D-brane and with explicitly broken kappa-symmetry. We show that the superconformal completion removes the logarithmic modular divergences that are present in the bosonic string loop scattering amplitudes. These features are all consequences of the relati…
