Harmonic superspaces from superstrings

Grassi, Pietro Antonio; Nieuwenhuizen, P. van

doi:10.1016/j.physletb.2004.04.051

Cited by 16 publications

(10 citation statements)

References 34 publications

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“…Consider now the space P 3 = CP 3 \CP 1 in which (λα) = 0. This space can be covered by two patches U + (λ1 = 0) and U − (λ2 = 0) with coordinates From (2.1) and (2.2), it is obvious that P 3 = U + ∪ U − coincides with the total space of the rank 2 holomorphic vector bundle 6 …”

Section: Local Coordinatesmentioning

confidence: 99%

“…Here, Y is a subspace of CP 3|4 parametrized by three complex bosonic coordinates together with their complex conjugate and four (holomorphic) fermionic coordinates, Ω is a holomorphic measure for bosonic and fermionic coordinates, andÂ 0,1 is the (0, 1)-component of a connection one-formÂ on a rank n complex vector bundle E over CP 3|4 depending on both the bosonic and fermionic coordinates. It was shown [2] that there is a bijection between the moduli spaces of hCS theory (1.2) on the supermanifold CP 3|4 \CP 1|4 and of self-dual N = 4 super-Yang-Mills (SYM) theory on the space R 4 with a metric of signature (+ + + +) or (− − + +), depending on the reality conditions imposed on the supertwistor space (for related works see [3][4][5][6][7][8][9][10]). It was also demonstrated that the above twistor description allows one to recover Yang-Mills scattering amplitudes, in particular, maximally helicity violating (MHV) ones, 2 and to clarify the holomorphicity…”

Section: Introductionmentioning

confidence: 99%

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On supertwistors, the Penrose--Ward transform and $\CN=4$ super-Yang--Mills theory

Popov¹,

Saemann²

2005

Advances in Theoretical and Mathematical Physics

108

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It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP 3|4 as a target space is equivalent to holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in turn is equivalent to self-dual N = 4 super-Yang-Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual N -extended SYM theory as the integrability of SYM fields on complex (2|N )-dimensional superplanes and demonstrate the equivalence of this description to Witten's formulation. The equivalence of the field equations of hCS theory on an open subset of CP 3|N to the field equations of self-dual N -extended SYM theory in four dimensions is made explicit. Furthermore, we extend the picture to the full N = 4 SYM theory and, by using the known supertwistor description of this case, we show that the corresponding constraint equations are (gauge) equivalent to the field equations of hCS theory on a quadric in CP 3|3 × CP 3|3 . e-print archive: http://lanl.arXiv.org/abs/arXiv:hep-th

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Section: Local Coordinatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On supertwistors, the Penrose--Ward transform and $\CN=4$ super-Yang--Mills theory

Popov¹,

Saemann²

2005

Advances in Theoretical and Mathematical Physics

108

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“…These distributions appear in the computation of Green functions. For recent explicit applications see for instance [59]- [61] and references therein.…”

Section: Integration Rulesmentioning

confidence: 99%

Topological string in harmonic space and correlation functions in stringy cosmology

Saidi¹,

Sedra²

2006

Nuclear Physics B

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We develop the harmonic space method for conifold and use it to study local complex deformations of T * S 3 preserving manifestly SL (2, C) isometry. We derive the perturbative manifestly SL (2, C) invariant partition function Z top of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c = 1 non critical theory are described by highest υ (n,0) and lowest components υ (0,n) of SL (2, C) spin s = n 2 multiplets υ (n−k,k) , 0 ≤ k ≤ n and are shown to be naturally captured by harmonic monomials. Isodoublets (n = 1) describe uncoupled units of momentum and winding modes and are exactly realized as the SL (2, C) harmonic variables U + α and V − α . We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T * S 1 (S 1 ) to the harmonic method on T * S 3 (S 3 ). The manifestly SU (2, C) covariant correlation functions of the S 3 quantum cosmology model of Gukov-Saraikin-Vafa are also studied. Keywords:harmonic analysis on conifold, topological string B model on T * S 3 , ground ring of 2D c = 1 string, Hartle-Hawking wave function and S 3 quantum cosmology. * h-saidi@fsr.ac.ma † sedra@ictp.it ± s,n . These vertex operators have conformal weights h, h = (1, 1) and are used in the study of infinitesimal deformations of above CFT 2 .

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“…First of all, we need to write the SO (10) representations such that we can extract SO(4) representations. By using the SU(4) notation of [18], the pure spinor λ α can be decomposed as…”

Section: Compactification To Four Dimensionsmentioning

confidence: 99%