Membranes and D-Branes |
In Ordinary Classical Physics
> s.a. black-hole geometry [membrane paradigm];
brane world; kaluza-klein theory.
* Idea: Submanifolds
of a manifold M considered as dynamical systems; D
is the dimension of the spatial cross-section.
@ Ordinary membranes: Carter CM(97)ht-in [dynamics];
McLaughlin AS(98) [nodes and nodal lines];
Pavšič ht/03-proc [background-independent];
Carter a1112-proc [classical brane dynamics];
Yan a1207 [dynamics, Born-Infeld-type wave equations].
@ Lagrangian / Hamiltonian formulation:
Aurilia & Christodoulou PLB(78),
JMP(79),
JMP(79);
Capovilla et al JPA(05);
Giachetta et al mp/06;
Zaripov G&C(07)-a0810 [conformally invariant].
@ D = 1 case, relativistic strings: He & Kong a1007 [in curved spacetime, and Cauchy problem];
> s.a. string theory.
Bosonic Fundamental Membranes
* Action: Can be the
Nambu-Goto type action, i.e., the induced metric on the world-tube, derivable
also as the effective action in field theory for domain walls, in some sense
analogous, or some other action with a cosmological term, or with extrinsic
curvature terms ("rigid membranes") (& Polyakov) (but these
seem hard to quantize consistently).
* Gauge: One can treat them in
the light cone gauge, but for p > 1 this is only a partial gauge
fixing, leaving still the so-called "area-preserving" diffeomorphisms
(for spherical spatial topology the structure constants are the same as those
of SU(∞) – Hoppe's theorem).
Supermembranes
* Action: In addition to
supersymmetry invariance, has an additional fermionic gauge invariance
("k-invariance"), as one can see for example from a
derivation of the effective action for domain walls in supersymmetric
quantum field theory.
* Relationships:
k-invariance for p = 2 in curved superspace implies
the field equations of 11D supergravity (is the latter a low-energy
limit of membranes?).
* Conditions/results:
Existence of a certain necessary form implies d − p
− 1 = n/4, where n is the dimensionality of the
spinor representation (number of fermionic coordinates in superspace?)
(recall though that a superparticle – i.e., p = 0 –
can live in any d); For p > 1, there is no spinning
p-brane.
@ References: Duff ht/96-ln;
Klusoň PRD(00)ht [non-BPS, action];
García del Moral FdP(09)-a0902 [quantum properties];
Michishita & Trzetrzelewski NPB(13) [ground state].
Quantization
* Renormalizability:
Membranes are not renormalizable in first quantization (worse than strings
in this respect), but one hopes for – and really only needs –
second quantization.
* Phenomenology: 1988,
Do there exist massless states? Several studies indicate the answer may
be no, but the issue is not settled.
* Anomalies: Only 11D
supermembranes (p = 2) have passed so far the tests for being
anomaly-free.
* Conclusion: 1988, So
far, no real motivation to consider them other than mathematical reasons;
Strings are physically better motivated and much more tractable.
Other References > s.a. branes [string-theory inspired brane world];
string theory [uniqueness] and phenomenology;
symplectic structures.
@ Intros, reviews: Polchinski ht/96-ln;
Bachas ht/98-ln;
Johnson ht/00-ln;
Carter IJTP(01)gq/00-in [classical];
Vancea ht/01;
Johnson 02,
06;
Hoppe JPA(13).
@ And curved spacetime: Duff ht/99-ln [black holes, AdS-cft];
Schomerus CQG(02)ht-ln;
> s.a. brane world gravity.
@ And cosmology: Bronnikov JMP(99);
> s.a. brane cosmology; kaluza-klein
theory; string phenomenology.
@ And geometry, quantum spacetime:
Mavromatos & Szabo ht/98-ln [non-commutative];
Douglas ht/99-ln.
@ Quantization: Smolin PRD(98)ht/97 [covariant];
Moncrief GRG(06) [ADM-type].
@ Related topics: Gueorguiev mp/02-conf,
mp/02-conf,
mp/05 [as reparametrization-invariant systems];
Roberts CEJP(11)ht/04 [fluid-like generalization].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 23 sep 2015