M-theory

M-theory issolution proposed forunknown theoryeverything which would combine all five superstring theories11-dimensional supergravity together. AccordingDr. Edward Witten, who proposedtheory, mathematical tools which have yetbe inventedneededorderfully understand it.

The following articlesomewhat technicalnature; see M-theory simplified forless technical article.

Tablecontents

1 M-theory's relationsuperstringssupergravity
2 CharacteristicsM-theory
3 Further Reading
4 External links

M-theory's relationsuperstringssupergravity

M-Theoryvarious geometric backgroundsassociated withdifferent superstring theories (in different geometric backgrounds),these limitsrelatedeach other byprincipleduality. Two physical theoriesdualeach other ifhave identical physics aftercertain mathematical transformation.

Type IIAIIBrelated by T-duality, as aretwo Heterotic theories. Type IHeterotic SO(32)related byS-duality. Type IIBalso S-dualitself.

The type II theories have two supersymmetries inten-dimensional sense,rest just one.
The type I theoryspecialthat itbased on unoriented openclosed strings.
The other fourbased on oriented closed strings.
The IIA theoryspecial because itnon-chiral (parity conserving).
The other fourchiral (parity violating).

In eachthese cases therean 11th dimension that becomes large at strong coupling. In the IIA case11th dimension iscircle. InHE caseisline interval, which makes eleven-dimensional space-time display two ten-dimensional boundaries. The strong coupling limiteither theory produces an 11-dimensional space-time. This eleven-dimensional description ofunderlying theorycalled "M- theory". A string's space-time history can be viewed mathematically by functions like

X^μ(σ,τ)

that describe howstring's two-dimensional sheet coordinates (σ,τ) map into space-time X^μ

One interpretationthis resultthat11th dimension was always present but invisible becauseradius of11th dimensionproportional tostring coupling contant andtraditional perturbative string theory presumes itbe infinitesimal. Another interpretationthat dimensionnotfundamental conceptM-theory at all.

CharacteristicsM-theory

M-theory contains much more than just strings. It contains both higherlower dimensional objects. These objectscalled p-branes where p denotes their dimensionality (thus, 1-brane forstring2-brane formembrane). Higher dimensional objects were always presentsuperstring theory but could never be studied beforeSecond Superstring Revolution becausetheir non-perturbative nature.

Insights into non-perturbative propertiesp-branes stem fromspecial classp-branes called Dirichlet p-branes (Dp-branes). This name results fromboundary conditions assigned toendsopen stringstype I superstrings.

Open strings oftype I theory can have endpoints which satisfyNeumann boundary condition. Under this condition,endpointsstringsfreemove about but no momentum can flow into or out ofend ofstring. The T duality infersexistenceopen stringspositions fixed indimensions thatT-transformed. Generally,type II theories, we can imagine open stringsspecific positions forend-pointssome ofdimensions. This lends an inference thatmust end onpreferred surface. Superficially, this notion seemsbreakrelativistic invariance oftheory, possibly leading toparadox. The resolutionthis paradoxthat strings end onp-dimensional dynamic object,Dp-brane.

The importanceD-branes stems fromfact thatmakepossiblestudyexcitations ofbrane usingrenormalizable 2D quantum field theory ofopen string instead ofnon-renormalizable world-volume theory ofD-brane itself. In this waybecomes possiblecompute non-perturbative phenomena using perturbative methods. Many ofpreviously identified p-branesD-branes ! OthersrelatedD-branes by duality symmetries, so thatcan also be brought under mathematical control. D-branes have found many useful applications,most remarkable beingstudyblack holes. StromingerVafa have shown that D-brane techniques can be usedcountquantum microstates associatedclassical black hole configurations. The simplest case first explored was static extremal charged black holesfive dimensions. StromingerVafa provedlarge values ofchargesentropy S = log N, where Nequal tonumberquantum states that system can be in, agrees withBekenstein-Hawking prediction (1/4area ofevent horizon).

This result has been generalizedblack holes4D as well asones thatnear extremal (and radiate correctly) or rotating,remarkable advance. It has not yet been proven that thereany problematic breakdownquantum mechanics dueblack holes.

Matrix theory (physics) ispromising formulationM-theory