This entry is about a D-brane species in string theory. For the items in the ADE-classification of name D4, see there.
The D-brane of dimension $4+1$ in type IIA string theory.
Khovanov homology has long been expected to appear as the observables in a 4-dimensional TQFT in higher analogy of how the Jones polynomial arises as an observable in 3-dimensional Chern-Simons theory. For instance for $\Sigma : K \to K'$ a cobordism between two knots there is a natural morphism
between the Khovanov homologies associated to the two knots.
In (Witten11) it is argued, following indications in (GukovSchwarzVafa) that this 4d TQFT is related to the worldvolume theory of the image in type IIA of D3-branes ending on NS5-branes in type IIB after one S-duality and one T-duality operation:
Earlier indication for this had come from the observation that Chern-Simons theory is the effective background theory for the A-model 2d TCFT (see TCFT – Worldsheet and effective background theories for details).
Notice that after the above T-duality operation the $(D4-D6)$-system wraps the $S^1$ (circle) along which the T-duality takes place.
Lifting that configuration to 11-dimensional supergravity gives M5-branes (the erstwhile D4-branes) on Taub-NUT ($\times S^1$). The M5-branes wrap the circle-fiber of Taub-NUT space, which shrinks to zero size at the origin (the MK6, the location of the erstwhile D6, which is where the D4s “end”). The low-energy theory, on a stack of M5-branes, is the 6d (2,0)-susy QFT.
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
As a Green-Schwarz sigma-model:
Mina Aganagic, Jaemo Park, Costin Popescu, John Schwarz, Section 6 of Dual D-Brane Actions, Nucl. Phys. B496 (1997) 215-230 (arXiv:hep-th/9702133)
Makoto Sakaguchi, IIB-Branes and New Spacetime Superalgebras, JHEP 0004 (2000) 019 (arXiv:hep-th/9909143)
The relation of the M5-brane to the D4-brane and the D=5 super Yang-Mills theory in its worldvolume theory by double dimensional reduction:
Eric Bergshoeff, Mees de Roo, Tomas Ortin, The Eleven-dimensional Five-brane (pdf)
Mina Aganagic, Jaemo Park, Costin Popescu, John Schwarz, Section 6 of World-Volume Action of the M Theory Five-Brane, Nucl.Phys. B496 (1997) 191-214 (arXiv:hep-th/9701166)
Neil Lambert, Constantinos Papageorgakis, Maximilian Schmidt-Sommerfeld, M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills, JHEP 1101:083 (2011) (arXiv:1012.2882)
Chong-Sun Chu, Sheng-Lan Ko, Non-abelian Action for Multiple Five-Branes with Self-Dual Tensors, (arXiv:1203.4224) JHEP05(2012)028
Neil Lambert, Miles Owen, Charged Chiral Fermions from M5-Branes (arXiv:1802.07766)
The relation to Khovanov homology
Last revised on July 23, 2019 at 05:18:02. See the history of this page for a list of all contributions to it.