Details
| Original language | English |
|---|---|
| Pages (from-to) | 931-998 |
| Number of pages | 68 |
| Journal | Advances in Theoretical and Mathematical Physics |
| Volume | 9 |
| Issue number | 6 |
| Publication status | Published - Dec 2005 |
Abstract
It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP3/4 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 CP3/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 CP3/3 × CP3/3.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Advances in Theoretical and Mathematical Physics, Vol. 9, No. 6, 12.2005, p. 931-998.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On supertwistors, the Penrose-Ward transform and N = 4 super-Yang-Mills theory
AU - Popov, Alexander D.
AU - Sämann, Christian
PY - 2005/12
Y1 - 2005/12
N2 - It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP3/4 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 CP3/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 CP3/3 × CP3/3.
AB - It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP3/4 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 CP3/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 CP3/3 × CP3/3.
UR - http://www.scopus.com/inward/record.url?scp=33748069269&partnerID=8YFLogxK
U2 - 10.4310/ATMP.2005.v9.n6.a2
DO - 10.4310/ATMP.2005.v9.n6.a2
M3 - Article
AN - SCOPUS:33748069269
VL - 9
SP - 931
EP - 998
JO - Advances in Theoretical and Mathematical Physics
JF - Advances in Theoretical and Mathematical Physics
SN - 1095-0761
IS - 6
ER -