Membranes
and D-Branes| Membranes
and D-Branes |
In Ordinary Classical Physics > s.a. branes; kaluza-klein.
* Idea: Submanifolds
of a manifold M considered as dynamical systems; D is
the dimension of the spatial cross-section.
@ Ordinary membranes: McLaughlin AS(98)
[nodes and nodal lines]; Pavsic ht/03-in
[background-independent].
@ Lagrangian/Hamiltonian formulation:
Aurilia & Christodoulou PLB(78), JMP(79), JMP(79);
Capovilla et al JPA(05);
Giachetta
et al mp/06.
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 susy invariance, has an additional fermionic gauge invariance ("k-invariance"),
as one can see e.g. from a derivation of the effective action for domain walls
in susy 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
dim 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;
Kluson PRD(00)ht [non-BPS,
action].
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 [uniqueness] and phenomenology;
symplectic structures.
@ Intros, reviews: Polchinski ht/96-ln;
Bachas ht/98-in;
Johnson ht/00-ln;
Carter IJTP(01)gq/00-in
[classical]; Vancea ht/01;
Johnson 02, 06.
@ 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, string
phenomenology.
@ And geometry, quantum spacetime: Mavromatos & Szabo ht/98-in
[non-commutative]; Douglas ht/99-in.
@ Quantization: Smolin PRD(98)ht/97 [covariant];
Moncrief GRG(06) [ADM-type].
@ Related topics: Carter ht/97-in
[dynamics]; Gueorguiev mp/02-in,
mp/02-in,
mp/05 [as
reparametrization-invariant systems]; Roberts
ht/04 [fluid-like
generalization].
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
27 jun 2008