nLab D6-D8-brane bound state

Idea

The special case of Dp-D(p+2)-brane bound state for D6-D8-brane bound states.

Properties

Flux density and Hanany Witten effect

See this section at Hanany-Witten effect.

Fuzzy funnel geometry

The fuzzy funnel/fuzzy 2-sphere noncommutative geometry of $D6\BOT d8$-brane intersections, from the point of the of the D6-brane non-abelian DBI-action (Gaiotto-Tomasiello 14, Fazzi 17, p. 41-46):

graphics grabbed from Fazzi 17, Fig. 3.14, taken in turn from Gaiotto-Tomasiello 14, Figure 5

graphics grabbed from Gaiotto-Tomasiello 14

The s-rule

By the s-rule a supersymmetric configurations of D6-branes stretching between NS5-branes and D8-branes has at most one D6-brane ending on any D8-brane:

graphics grabbed from Fazzi 17

graphics grabbed from Gaiotto-Tomasiello 14

graphics grabbed from GKSTY 02

As QCD Monopoles in the Witten-Sakai-Sugimoto model

Generally Dp-D(p+2)-brane intersections geometrically engineer Yang-Mills monopoles in the worldvolume of the higher dimensional D$(p+2)$-branes.

Specifically for $p = 6$, i.e. for D6-D8-brane intersections, this fits with the Witten-Sakai-Sugimoto model geometrically engineering quantum chromodynamics, and then gives a geometric engineering of the Yang-Mills monopoles in actual QCD (HLPY 08, p. 16).

graphics from Sati-Schreiber 19c

Here we are showing

1. the color D4-branes;

2. the flavor D8-branes;

   with

   1. the 5d Chern-Simons theory on their worldvolume

   2. the corresponding 4d WZW model on the boundary

   both exhibiting the meson fields

3. the baryon D4-branes

   (see below at WSS – Baryons)

4. the Yang-Mills monopole D6-branes

   (see at D6-D8-brane bound state)

5. the NS5-branes.

Related concepts

brane intersections/bound states/wrapped branes/polarized branes

• D-branes and anti D-branes form bound states by tachyon condensation, thought to imply the classification of D-brane charge by K-theory

• intersecting D-branes/fuzzy funnels:

  • Dp-D(p+2)-brane bound state and Yang-Mills monopoles

    • D0-D2 brane bound state

    • D1-D3 brane bound state

    • D2-D4 brane bound state

    • D3-D5 brane bound state

    • D4-D6 brane bound state

    • D6-D8-brane bound state

  • Dp-D(p+4)-brane bound state and Yang-Mills instantons

    • D0-D4 brane bound state

    • D1-D5 brane bound state

    • D2-D6 brane bound state

    • D3-D7 brane bound state

    • D4-D8 brane bound state

    • D5-D9 brane bound state

      small instanton

• Dp-D(p+6) brane bound state

  • D0-D6 brane bound state

  • D1-D7 brane bound state

  • D2-D8 brane bound state

• NS5-D4-D2 bound states

• Hanany-Witten effect

S-duality$\,$bound states:

• (p,q)-string

• (p,q)5-branes

• string network

• 5-brane web

intersecting$\,$M-branes:

• M5-MO9 brane bound state

• M2-M5 brane bound state

  • M-string, E-string

• membrane triple junction

References

As black brane solutions

On D6-D8-brane bound states as black brane-solutions in massive type IIA string theory:

• Harvendra Singh, Duality symmetric massive type II theories in $D=8$ and $D=6$, JHEP 0204:017, 2002 (arXiv:hep-th/0109147)

• Harvendra Singh, Note on (D6,D8) Bound State, Massive Duality and Non-commutativity, Nucl. Phys. B661 (2003) 394-408 (arXiv:hep-th/0212103)

• Fabio Apruzzi, Marco Fazzi, Dario Rosa, Alessandro Tomasiello, All $AdS_7$ solutions of type II supergravity, JHEP 04 (2014) 064 (arxiv:1309.2949)

With emphasis on charge quantization of the RR-field flux forms via bundle gerbes:

• Jussi Kalkkinen, Gerbes and Massive Type II Configurations, JHEP 9907 :002, 1999 (arXiv:hep-th/9905018)

With emphases of the fuzzy funnel noncommutative geometry:

• Davide Gaiotto, Alessandro Tomasiello, Holography for $(1,0)$ theories in six dimensions, JHEP 12 (2014) 003 (arXiv:1404.0711)

• Marco Fazzi, p. 41-46 of: Higher-dimensional field theories from type II supergravity (arxiv:1712.04447)

In view of AdS/CFT:

• Fabio Apruzzi, Giuseppe Dibitetto, Luigi Tizzano, A new 6d fixed point from holography, JHEP 11 (2016) 126 (arxiv:1603.06576)

• Nikolay Bobev, Giuseppe Dibitetto, Fridrik Freyr Gautason, Brecht Truijen, Holography, Brane Intersections and Six-dimensional SCFTs, JHEP 1702 (2017) 116 (arxiv:1612.06324)

$AdS_3/CFT_2$ on D2/D4-D6/D8 branes

On black$\;$D6-D8-brane bound states in massive type IIA string theory, with defect D2-D4-brane bound states inside them realizing AdS3-CFT2 as defect field theory “inside” AdS7-CFT6:

• Giuseppe Dibitetto, Nicolò Petri, 6d surface defects from massive type IIA, JHEP 01 (2018) 039 (arxiv:1707.06154)

• Nicolò Petri, section 6.5 of: Supersymmetric objects in gauged supergravities (arxiv:1802.04733)

• Nicolò Petri, Surface defects in massive IIA, talk at Recent Trends in String Theory and Related Topics 2018 (pdf)

• Giuseppe Dibitetto, Nicolò Petri, $AdS_3$ vacua and surface defects in massive IIA (arxiv:1904.02455)

• Yolanda Lozano, Niall Macpherson, Carlos Nunez, Anayeli Ramirez, $1/4$ BPS $AdS_3/CFT_2$ (arxiv:1909.09636)

• Yolanda Lozano, Niall Macpherson, Carlos Nunez, Anayeli Ramirez, Two dimensional $N=(0,4)$ quivers dual to $AdS_3$ solutions in massive IIA (arxiv:1909.10510)

• Yolanda Lozano, Niall Macpherson, Carlos Nunez, Anayeli Ramirez, $AdS_3$ solutions in massive IIA, defect CFTs and T-duality (arxiv:1909.11669)

• Kostas Filippas, Non-integrability on $AdS_3$ supergravity (arxiv:1910.12981)

See also

• Andrea Legramandi, Niall Macpherson, $AdS_3$ solutions with $\mathcal{N}=(3,0)$ from $S^3 \timesS^3$ fibrations, (arXiv:1912.10509

The T-duality to AdS2/CFT1:

• Yolanda Lozano, Carlos Nunez, Anayeli Ramirez, Stefano Speziali, New $AdS_2$ backgrounds and $\mathcal{N}=4$ Conformal Quantum Mechanics (arXiv:2011.00005)

Hanany-Witten effect

On the Hanany-Witten effect for NS5/D6/D8-branes:

• Amihay Hanany, Alberto Zaffaroni, §2.4 Chiral Symmetry from Type IIA Branes, Nucl. Phys. B 509 (1998) 145-168 [arXiv:hep-th/9706047, doi:10.1016/S0550-3213(97)00595-6]

• Eric Bergshoeff, Yolanda Lozano, Tomas Ortin, p. 60 of: Massive Branes, Nucl. Phys. B 518 (1998) 363-423 [arXiv:hep-th/9712115, doi:10.1016/S0550-3213(98)00045-5]

In geometric engineering of monopoles

For transversal D6-D8-brane bound states with an eye towards describing Yang-Mills monopoles:

with an emphasis of half NS5-brane in type I' string theory:

• Amihay Hanany, Alberto Zaffaroni, Monopoles in String Theory, JHEP 9912 (1999) 014 (arxiv:hep-th/9911113)

with an emphasis on holographic QCD:

• Deog Ki Hong, Ki-Myeong Lee, Cheonsoo Park, Ho-Ung Yee, Section V of: Holographic Monopole Catalysis of Baryon Decay, JHEP 0808:018, 2008 (arXiv:0804.1326)

For more see the references at Dp-D(p+2)-brane bound states.

Relation to Seiberg-Witten curves

On quantum Seiberg-Witten curves of E-string-theories in relation to D6-D8-brane bound states:

• Jin Chen, Babak Haghighat, Hee-Cheol Kim, Marcus Sperling, Xin Wang, E-string Quantum Curve, Nuclear Physics B 973 (2021) 115602 [arXiv:2103.16996, doi:10.1016/j.nuclphysb.2021.115602]