Harmonic superspaces of extended supersymmetry. I. The calculus of harmonic variables

We study the N =4 harmonic superparticle model, both with and without central charge and quantize it. Since the central charge breaks the U (4) R-symmetry group of the N =4 superalgebra down to U Sp(4), we consider the superparticle dynamics in N =4 harmonic superspace with U Sp(4)/(U (1) × U (1)) harmonic variables. We show that the quantization of a massive superparticle with central charge leads to a superfield realization of the N =4 massive vector multiplet in N =4 harmonic superspace. In the massless case without central charge the superparticle quantization reproduces three different multiplets: the N =4 SYM multiplet, the N =4 gravitino multiplet and N =4 supergravity multiplet. The SYM multiplet is described by six analytic superfield strengths with different types of analyticity. We show that these strengths solve the N =4 SYM constraints and can be used for the construction of actions in N =4 harmonic superspace.

Section: Introductionmentioning

confidence: 99%

superparticle and super-Yang–Mills theory in harmonic superspace

Buchbinder¹,

Lechtenfeld²,

Samsonov³

2008

“…Since the R-symmetry group is SU(4), the harmonic coordinates that we introduce will form the coset manifold SU(4)/H, where H is a subgroup of SU(4). As has been discussed in [67], there are several possibilities for the choice of H, which are suitable for different physical contexts (see e.g. [11] for one particular application).…”

Section: B1 Harmonic Coordinatesmentioning

confidence: 99%

BPS-saturated string amplitudes: K3 elliptic genus and Igusa cusp form χ10

Hohenegger

Stieberger

2012

We study BPS saturated one-loop amplitudes in type II string theory compactified on K3 × T 2 . The classes of amplitudes we consider are only sensitive to the very basic topological data of the internal K3 manifold. As a consequence, the integrands of the former are related to the elliptic genus of K3, which can be decomposed into representations of the internal N = 4 superconformal algebra. Depending on the precise choice of external states these amplitudes capture either only the contribution of the short multiplets or the full series including intermediate multiplets. In the latter case we can define a generating functional for the whole class, which we show is given by the weight ten Igusa cusp form χ 10 of Sp(4, Z). We speculate on possible algebraic implications of our result on the BPS states of the N = 4 type II compactification. a shoheneg@mppmu.mpg.de b stephan.stieberger@mpp.mpg.de

“…Using the covariant derivatives and solving the Bianchi identities, we can immediately write down the supersymmetry transformations (2) By analogy with the case of the N = 2 models with the intrinsic central charge [12]- [15], the equations (14,18,19) can be called the generalized Dirac equation, the Yang-Mills equation and the Klein-Gordon equation respectively. Thus the central charge plays the role of 'fifth coordinate'.…”

mentioning

confidence: 99%

“…As a consequence of (9)- (19), we can construct the complete power expansion of the 1) . The set of constraints (9)- (19) shows that the component fields in [1] are completely determined by the lowest orders in the expansion W ij (x, θ,θ, z) over z, θ,θ. Then it is clear that we can completely fix the dependence of all quantities under consideration on the central-charge coordinate z, as was done for the theories with N = 2 rigid supersymmetry with the central charge [12], [14], [15].…”

mentioning

confidence: 99%

“…They are the consequences of the restrictions (20), which should be added to the identities (8), (11) if we want to reduce the USp(4) SYM theory to the on-shell SU(4) SYM theory. In this case the identities (14), (17), (18), (19) are converted into equations of motion for conventional N = 4 SYM theory. If we do not impose the conditions (20), we have the USp (4) superfield gauge theory satisfying the identities (9) - (19).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Towards harmonic superfield formulation of N=4, USp(4) SYM theory with the central charge

Buchbinder

Плетнев

2013

We develop a superfield formulation of N = 4 supersymmetric Yang-Mills theory with the rigid central charge in U Sp(4) harmonic superspace. The component formulation of this theory was given by Sohnius, Stelle and West [1], but its superfield formulation has not been constructed so far. We construct the superfield action, corresponding to this model, and show that it reproduces the component action from [1].