In theoretical physics, an M2-brane, is a spatially extended mathematical object (brane) that appears in string theory and in related theories (e.g. M-theory, F-theory). In particular, it is a solution of eleven-dimensional supergravity which possesses a three-dimensional world volume.
Description
The M2-brane solution can be found[1] by requiring \( (Poincare)_{{3}}\times SO(8) \) symmetry of the solution and solving the supergravity equations of motion with the p-brane ansatz. The solution is given by a metric and three-form gauge field which, in isotropic coordinates, can be written as
\( {\begin{aligned}ds_{{M2}}^{{2}}&=\left(1+{\frac {q}{r^{{6}}}}\right)^{{-{\frac {2}{3}}}}dx^{{\mu }}dx^{{\nu }}\eta _{{\mu \nu }}+\left(1+{\frac {q}{r^{{6}}}}\right)^{{{\frac {1}{3}}}}dx^{{i}}dx^{{j}}\delta _{{ij}}\\F_{{i\mu _{{1}}\mu _{{2}}\mu _{{3}}}}&=\epsilon _{{\mu _{{1}}\mu _{{2}}\mu _{{3}}}}\partial _{{i}}\left(1+{\frac {q}{r^{6}}}\right)^{{-1}},\quad \mu =1,\ldots ,3\quad i=4,\ldots ,11,\end{aligned}} \)
where η {\displaystyle \eta } \eta is the flat-space metric and the distinction has been made between world volume \( x^\mu \) and transverse \( x^{i} \) coordinates. The constant q is proportional to the charge of the brane which is given by the integral of F over the boundary of the transverse space of the brane.[2]
See also
String theory
Membrane (M-theory)
M-theory
References
K. Stelle, "BPS Branes in Supergravity"
A. Miemiec, I. Schnakenburg "Basics of M-theory"
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String theory
Background
Strings History of string theory
First superstring revolution Second superstring revolution String theory landscape
Calabi-Yau-alternate
Theory
Nambu–Goto action Polyakov action Bosonic string theory Superstring theory
Type I string Type II string
Type IIA string Type IIB string Heterotic string N=2 superstring F-theory String field theory Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism
String duality
T-duality S-duality U-duality Montonen–Olive duality
Particles and fields
Graviton Dilaton Tachyon Ramond–Ramond field Kalb–Ramond field Magnetic monopole Dual graviton Dual photon
Branes
D-brane NS5-brane M2-brane M5-brane S-brane Black brane Black holes Black string Brane cosmology Quiver diagram Hanany–Witten transition
Conformal field theory
Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten model
Gauge theory
Anomalies Instantons Chern–Simons form Bogomol'nyi–Prasad–Sommerfield bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics
Geometry
Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold
Calabi–Yau manifold Hyperkähler manifold
K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten domain wall K-theory (physics) Twisted K-theory
Supergravity Superspace Lie superalgebra Lie supergroup
Holography
Holographic principle AdS/CFT correspondence
M-theory
Matrix theory Introduction to M-theory
String theorists
Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Cleaver Curtright Dijkgraaf Distler Douglas Duff Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey Hořava Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind 't Hooft Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach
Hellenica World - Scientific Library
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