nLab Myers effect

Idea

What is called the Myers effect (Myers 99) in string theory is the phenomenon that given $N$ D0-branes in a constant background RR field $F_4$ (the field strength associated with D2-brane charge) with, crucially, nonabelian effects included via a nonabelian DBI action, then these D0-branes expand into a fuzzy 2-sphere which represents a spherical D0-D2 brane bound state of a D2-brane and $N$ D0-branes (Myers 99, section 6, see p. 21 (22 of 33), Myers 03, section 4).

Analogous polarization effects are thought to exists for branes of other dimensions, for instance polarizing D2-branes into D4-branes etc, and notably for M2-branes to polarize into M5-branes (Bena 00, review in BLMP 13, Section 6). In each case the higher dimensional brane ends up wrapping a cycle which is topologically trivial (hence in principle shrinkable) but flux through this cycle exerts a force that stabilizes the brane against collapsing on this cycle.

A closely related stabilization mechanism is that of branes turned into “giant gravitons”, where the stabilizing role of flux is instead taken by angular momentum (typically along the equator of an n-sphere in a Freund-Rubin compactification).

Related concepts

• giant graviton

• fuzzy funnel

• dyon

• BFSS matrix model, BMN matrix model

• wrapped brane, brane intersection

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

Polarization of D-branes

Precursor discussion appears in

• Roberto Emparan, Born-Infeld Strings Tunneling to D-branes, Phys. Lett. B423 (1998) 71-78 (arXiv:hep-th/9711106)

The effect now known as the “Myers effect” in D-brane theory was first described in:

• Robert Myers, Dielectric-Branes, JHEP 9912 (1999) 022 (arXiv:hep-th/9910053)

for the case of D0-branes polarizing to D0-D2 brane bound states.

Review:

• Robert Myers, Section 4 of: Nonabelian Phenomena on D-branes, Class. Quant. Grav. 20 (2003) S347-S372 (arXiv:hep-th/0303072)

See also:

• Z. Guralnik, Sanyaje Ramgoolam, On the Polarization of Unstable D0-Branes into Non-Commutative Odd Spheres, JHEP 0102:032, 2001 (arXiv:hep-th/0101001)

• Pedro J. Silva, Quantum Myers effect and its supergravity dual for D0/D4 systems (arXiv:hep-th/0109112)

• Yoshifumi Hyakutake, Gravitational Dielectric Effect and Myers Effect, Phys. Rev. D71:046007, 2005 (arXiv:hep-th/0401026)

Discussion of D-brane polarization on curved spacetime in context of the AdS/QCD correspondence:

• Joseph Polchinski, Matthew Strassler, The String Dual of a Confining Four-Dimensional Gauge Theory (arXiv:hep-th/0003136)

• Ofer Aharony, Arvind Rajaraman, String Theory Duals for Mass-deformed $SO(N)$ and $USp(2N)$ $\mathcal{N}=4$ SYM Theories, Phys. Rev. D62:106002, 2000 (arXiv:hep-th/0004151)

• Iosif Bena, Stanislav Kuperstein, Brane polarization is no cure for tachyons, JHEP09 (2015) 112 (arXiv:1504.00656)

Discussion of D2-branes polarizing to D2-D4 brane bound states:

• Iosif Bena, Aleksey Nudelman, Warping and vacua of $(S)YM_{3+1}$, Phys. Rev. D62 (2000) 086008 (arXiv:hep-th/0005163)

• Iosif Bena, Aleksey Nudelman, Exotic polarizations of D2 branes and oblique vacua of $(S)YM_{2+1}$, Phys. Rev. D62 (2000) 126007 (arXiv:hep-th/0006102)

Polarization into torus shape:

• Yoshifumi Hyakutake, Torus-like Dielectric D2-brane, JHEP 0105:013, 2001 (arXiv:hep-th/0103146)

• Tatsuma Nishioka, Tadashi Takayanagi, Fuzzy Ring from M2-brane Giant Torus, JHEP 0810:082, 2008 (arXiv:0808.2691)

Discussion of D4-branes polarizing into NS5-branes:

• Iosif Bena, Calin Ciocarlie, Exact $\mathcal{N}=2$ Supergravity Solutions With Polarized Branes, Phys. Rev. D70 (2004) 086005 (arXiv:hep-th/0212252)

• Iosif Bena, Radu Roiban, $\mathcal{N}=1^\ast$ in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler, JHEP 0311 (2003) 001 (arXiv:hep-th/0308013)

Polarization of fractional D-branes:

• Timothy J. Hollowood, S. Prem Kumar, World-sheet Instantons via the Myers Effect and $\mathcal{N} = 1^\ast$ Quiver Superpotentials, JHEP 0210:077, 2002 (arXiv:hep-th/0206051)

D-brane polarization into supertubes

• David Mateos, Paul Townsend, Supertubes, Phys. Rev. Lett. 87 (2001) 011602 (arXiv:hep-th/0103030)

• Martin Kruczenski, Robert Myers, Amanda Peet, David J. Winters, Aspects of supertubes, JHEP 0205:017, 2002 (arXiv:hep-th/0204103)

Polarization of M2-branes into M5-branes

The Myers effect in M-theory for M2-branes polarizing into M5-branes of (fuzzy) 3-sphere-shape (M2-M5 brane bound states):

• Iosif Bena, The M-theory dual of a 3 dimensional theory with reduced supersymmetry, Phys. Rev. D62:126006, 2000 (arXiv:hep-th/0004142)

• Iosif Bena, Nicholas Warner, A harmonic family of dielectric flow solutions with maximal supersymmetry, JHEP 0412:021, 2004 (arXiv:hep-th/0406145)

• Masato Arai, Claus Montonen, Shin Sasaki, Vortices, Q-balls and Domain Walls on Dielectric M2-branes, JHEP 0903:119, 2009 (arXiv:0812.4437)

• Iosif Bena, Mariana Graña, Stanislav Kuperstein, Stefano Massai, Tachyonic Anti-M2 Branes, JHEP 1406:173, 2014 (arXiv:1402.2294)

With emphasis on the role of the Page charge/Hopf WZ term:

• Krzysztof Pilch, Alexander Tyukov, Nicholas Warner, Flowing to Higher Dimensions: A New Strongly-Coupled Phase on M2 Branes, JHEP11 (2015) 170 (arXiv:1506.01045)

The corresponding D2-NS5 bound state under duality between M-theory and type IIA string theory:

• Iosif Bena, Aleksey Nudelman, Warping and vacua of $(S)YM_{3+1}$, Phys. Rev. D62 (2000) 086008 (arXiv:hep-th/0005163)

Via the mass-deformed ABJM model:

• Jaume Gomis, Diego Rodriguez-Gomez, Mark Van Raamsdonk, Herman Verlinde, A Massive Study of M2-brane Proposals, JHEP 0809:113, 2008 (arXiv:0807.1074)

and identifying the polarization into $S^3$ as a fuzzy sphere-version of the complex Hopf fibration:

• Horatiu Nastase, Constantinos Papageorgakis, Sanjaye Ramgoolam, The fuzzy $S^2$ structure of M2-M5 systems in ABJM membrane theories, JHEP 0905:123, 2009 (arXiv:0903.3966)

Review in:

• Jonathan Bagger, Neil Lambert, Sunil Mukhi, Constantinos Papageorgakis, Section 6 of: Multiple Membranes in M-theory, Physics Reports, Volume 527, Issue 1, 1 June 2013, Pages 1-100 (arXiv:1203.3546, doi:10.1016/j.physrep.2013.01.006)

Polarization of M5-branes into MK6s

More general M-brane polarizations and polarization of M5-branes into MK6s:

• Yolanda Lozano, Non-commutative Branes from M-theory, Phys. Rev. D64 (2001) 106011 (arXiv:hep-th/0012137)

• Iosif Bena, Diana Vaman, The polarization of M5 branes and little string theories with reduced supersymmetry, JHEP 0111 (2001) 032 (arXiv:hep-th/0101064)

Via the ABJM model:

• Wung-Hong Huang, KK6 from M2 in ABJM, JHEP 1105:054, 2011 (arXiv:1102.3357)

• Wung-Hong Huang, M2-KK6 System in ABJM Theory: Fuzzy $S^3$ and Wrapped KK6 (arXiv:1107.2030)

Relation to giant gravitons

On the relation of polarized branes to giant gravitons:

• Iosif Bena, Douglas Smith, Towards the solution to the giant graviton puzzle, Phys.Rev. D71 (2005) 025005 (arXiv:hep-th/0401173)

In the BMN matrix model

On solutions of the BMN matrix model in relation to the Myers effect and D0-D2 brane bound states:

• Hai Lin, The Supergravity Dual of the BMN Matrix Model, JHEP 0412:001, 2004 (arXiv:hep-th/0407250)