Contents

# Contents

## 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).

brane intersections/bound states/wrapped branes/polarized branes

S-duality$\,$bound states:

intersecting$\,$M-branes:

## References

### Polarization of D-branes

Precursor discussion appears in

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

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

Review:

See also:

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

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)

### 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):

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

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:

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

Review in:

### Polarization of M5-branes into MK6s

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

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:

### 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)

Last revised on March 6, 2021 at 09:44:41. See the history of this page for a list of all contributions to it.