On Supertwistors, the Penrose-Ward Transform and N=4 super Yang-Mills Theory (original) (raw)
Related papers
On supertwistors, the Penrose--Ward transform and CN=4\CN=4CN=4 super-Yang--Mills theory
Advances in Theoretical and Mathematical Physics, 2005
It was recently shown by Witten that B-type open topological string theory with the supertwistor space P 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 super Yang-Mills 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 P 3|N to the field equations of selfdual 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 P 3|3 × P 3|3
N=2 Superstring Theory Generates Supersymmetric Chern-Simons Theories
Modern Physics Letters A, 1994
We show that the action of self-dual supersymmetric Yang-Mills theory in four dimensions, which describes the consistent massless background fields for N=2 superstring, generates the actions for N=1 and N=2 supersymmetric non-Abelian Chern-Simons theories in three dimensions after some dimensional reductions. Since the latters play important roles for supersymmetric integrable models, this result indicates the fundamental significance of the N=2 superstring theory controlling (possibly all) supersymmetric integrable models in lower dimensions.
Journal of High Energy Physics, 2005
In this paper, we propose so-called fattened complex manifolds as target spaces for the topological B-model. We naturally obtain these manifolds by restricting the structure sheaf of the N = 4 supertwistor space, a process, which can be understood as a fermionic dimensional reduction. Using the twistorial description of these fattened complex manifolds, we construct Penrose-Ward transforms between solutions to the holomorphic Chern-Simons equations on these spaces and bosonic subsectors of solutions to the N = 4 self-dual Yang-Mills equations on 4 or Ê 4 . Furthermore, we comment on Yau's theorem for these spaces.
Duality in twisted = 4 supersymmetric gauge theories in four dimensions
Nuclear Physics B, 1999
We consider a twisted version of the four-dimensional N = 4 supersymmetric Yang-Mills theory with gauge groups SU(2) and SO(3), and bare masses for two of its chiral multiplets, thereby breaking N = 4 down to N = 2. Using the wall-crossing technique introduced by Moore and Witten within the u-plane approach to twisted topological field theories, we compute the partition function and all the topological correlation functions for the case of simply-connected spin fourmanifolds of simple type. By including 't Hooft fluxes, we analyse the properties of the resulting formulae under duality transformations. The partition function transforms in the same way as the one first presented by Vafa and Witten for another twist of the N = 4 supersymmetric theory in their strong coupling test of S-duality. Both partition functions coincide on K3. The topological correlation functions turn out to transform covariantly under duality, following a simple pattern which seems to be inherent in a general type of topological quantum field theories.
𝒩 = 8 superconformal Chern-Simons theories
Journal of High Energy Physics, 2008
A Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL). The BL theory has SO(4) gauge symmetry and contains scalar and spinor fields that transform as 4-vectors. We verify that this theory has OSp(8|4) superconformal symmetry and that it is parity conserving despite the fact that it contains a Chern-Simons term. We describe several unsuccessful attempts to construct theories of this type for other gauge groups and representations. This experience leads us to conjecture the uniqueness of the BL theory. Given its large symmetry, we expect this theory to play a significant role in the future development of string theory and M-theory.
4-D semistrict higher Chern-Simons theory I
Journal of High Energy Physics, 2014
We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory. Its symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant non singular bilinear form. We analyze the gauge invariance of the theory and show that action is invariant under a higher gauge transformation up to a higher winding number. We find that the theory admits two seemingly inequivalent canonical quantizations. The first is manifestly topological, it does not require a choice of any additional structure on the spacial 3-fold. The second, more akin to that of ordinary Chern-Simons theory, involves fixing a CR structure on the latter. Correspondingly, we obtain two sets of semistrict higher WZW Ward identities and we find the explicit expressions of two higher versions of the WZW action. We speculate that the model could be used to define 2-knot invariants of 4-folds.
Dual expansions of super Yang–Mills theory via IIB superstring theory
Nuclear Physics B, 2000
We examine the dual correspondence between holographic IIB superstring theory and N = 4 super Yang-Mills theory at finite values of the coupling constants. In particular we analyze a field theory strong-coupling expansion which is the S-dual of the planar expansion. This expansion arises naturally as the AdS/CFT dual of the IIB superstring scattering amplitudes given a genus truncation property due to modular invariance. The space-time structure of the contributions to the field theory four-point correlation functions obtained from the IIB scattering elements is investigated in the example of the product of four conserved stress tensors, and is expressed as an infinite sum of field theory triangle integrals. The OPE structure of these contributions to the stress tensor four-point function is analyzed and shown not to give rise to any poles. Quantization of the string in the background of a five-form field strength is performed through a covariantized background field approach, and relations to the N = 4 topological string are found.
ℵ0-extended supergravity and Chern-Simons theories
Nuclear Physics B, 1996
We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in threedimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ 0 (Aleph-Null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ 0 supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three-dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ 0 globally and locally supersymmetric theories in three-dimensions. As an interesting application, we present ℵ 0 supergravity Liouville theory in two-dimensions after appropriate dimensional reduction from threedimensions.