The Deconfinement Phase Transition and Thermal String Theory

1

• Matrix Theory and the Fundamental Symmetry
  
• A Planck Scale Generalized Electric Magnetic
  Dual Initial State
• (Chronology Gregory Moore, Jeffrey Harvey,
  Algebra BPS States, N2 String theory. Th/9510182
  (Conjecture Dual string theories are
  manifestations of a single Algebra.)
• Brief review of Peter Wests elucidation of the
  principle that M theory, as the completion of 11d
  supergravity, a theory with 32 supercharges, is
  the very extended Kac-Moody group .(Peter
  West, 0402140).
• The 10d anomaly free completion of this theory
  is , with 16 conserved
  supercharges, and affine E8xE8. (Chaudhuri,
  2004).
• A matrix realization of this algebra on a Planck
  sized region of spacetime is conjectured to be
  generalized EM selfdual Initial State Universe
  with the generalized electric magnetic self dual
  spectrum of 12 pforms.
• (Chaudhuri, 2004, 2008-10.)
• IV. Conclusions Conjectures and Future Work.
• (Hidden Symmetry Unmasked E11 Matrix
  Theory, hep-th/0404235, Chaudhuri).

2
Fundamental Symmetry for Theories with 32
Supercharges Theory Space or Vacuum
Manifold ? A Unifying Algebra ensures
Completeness. Dimensional Reduction of
Supergravities on T_n Cremmer -Julia En Series.
(1981). ----begin with T-duality group,
observe that E11 contains both O(10-n, 10-n) and
GL(11-n,R) as proper subgroups
----in 6d and below, dualize the NS-NS and R-R
fields to extend T-duality to the Cremmer-Julia
group D9 GL(2,R) SL(n,R)xR D8
SL(3,R)xSL(2,R)
D7 SL(5,R) D6
SO(5,5)
D5 E_(6,6)
D4 E_(7,7)

D3 E_(8,8) Dlt3 requires string
theory. Nicolai demonstrates E9 in 2d, with
SO(2,1) x SO(16) hidden structure 11d sugra.E10
conjectured symmetry algebra for Type II
toroidally compactified space. Moore 1993. Type
IIA-Heterotic 6d effective String duality sheds
light on compactifications to 2d, fit neatly
within the Monster Group, M_24 is this too
large?? Lowe Chaudhuri, 1995. Algebra BPS
States,N2 Heterotic String,8 conserved
supercharges. Moore Harvey, 95. (a) Vacuum
structure that of a groupoid, unlike tori K3 x
T2. E10 embedded in gauge and supergravity
sectors. (b) Monopoles of the generalized Kac
Moody algebra govern the nonperturbative
properties, as in Seiberg Witten theory. (c)
Multiplicity of Low energy Effective Dual string
and field theories are realizations of a
generalized Kac Moody Algebra.
3
Peter West elucidated the principle that M
theory is the group E11 the elements in the
Chevalley basis of E11 can be shown to be
isomorphic to the generators of the global
algebra of each of the theories with 32
supercharges 11d sugra, 10d type IIA, type IIB,
and massive type IIA. Hep-th/0402142. E11 is the
very extended termination of C-J Series, a
generalized Kac Moody algebra of rank 11 with
root lattice composed from.. As for E10, the
(1,1) lattices of indefinite signature give real
and imaginary roots the representation theory
is subtle. Bosonic E11 has a Minkowskian
supersymmetric extension for spacetimes of
signature (1,10)/(1,9). Schnakenburg West
2002-04 (a) enumerate the volume preserving
basis for Lorentz generators, GL(d,R) SL(d,R) x
R d11, 10 and the full set of pform
supergravity potentials, Neveu-Schwarz and
Ramond-Ramond, include dilaton-axion 10d. (b)
compute explicit structure constants of each 10,
11d supergravity global algebras.(c) identify the
isomorphismfrom each Cartan subalgebra to the
Chevalley basis of . Additional Evidence
invoke the nonlinear realization to identify
explicit roots of E_11 with known line elements
of supergravity M backgrounds.
Unifying Symmetry for Theories with 32
Supercharges
4
Unifying Symmetry for Theories with 32
Supercharges ----due to the KMA level structure,
tower of fields as an extension of supergravity
alone. No coupling to Yang Mills fields,
nor chiral matter fields. Romans type IIA
mass.

Extending the global algebra of
non-chiral IIA by a central extension gives
Massive II --to develop a comparison
string theory, we still need to introduce
spacetime, and mass parameters, namely, the
string tension. This bosonic Algebraic theory is
topological Suppressing the algebra of the
Lorentz (volume preserving) generators..Massive
IIA!
-----The 11d sugra and Type IIA T
duality group contained in E_11, and Type IIB is
a simple modification of the Dynkin diagram of
E_11 begin with E_8, extend to affine E_8 (E_9),
and on to hyperbolic E_10, E_11. The Dynkin
diagram E_11 bifurcates at the 8th (very
extended) node two inequivalent embeddings of
the subgroup A_10, associated to the Lorentz
algebra of 10d Type IIA and Type IIB.


5
Global Algebra of the Type IIB Theory Peter
Wests elucidation of the principle that M theory
is E11 was based in part simple observation E_11
Dynkin diagram has 2 inequivalent A9 chains,
bifurcating at node 8. Map from global type IIA
to the Canonical (Chevalley) Basis
----Unlike type IIA, the spinors of IIB have
identical chirality, no permissible extension of
the supersymmetry algebra by a mass (Romans)
parameter. -----Remarkably, the IIB
algebra has a straightforward truncation given by
the orientation projection to the global algebra
of the type IB supergravity, breaking the SL(2,Z)
symmetry, keeping a single term from each
doublet.

6
Theo of 16 Supercharges the Fundamental
Symmetry Note! The
projection acting on type IIB superstring acts on
the global algebra of the type IIB supergravity,
breaking the SL(2,Z) symmetry, yields Type IB
This truncation is readily identified as
D_11, with dilaton, 2form (NS/RR) 6,8form duals.
Thehe algebra of generators of gauge symmetries
does not mix with the Lorentz-supergravity-pform
potentials in theories of 16 supercharges, the
anomaly free extension is affine E8XE8.

(Chaudhuri, April 2004,
0404235). Note the absence of spacetime in the
Algebraic formulation, modifying Wests
conjecture, we can state String/M theory is a
realization of the Algebra
extended by Supersymmetry with 16 conserved
supercharges. Requires Minkowskian signature
(1,9). Aside With E_11, (1,10) gives an
unambiguous bosonic algebra, Euclidean signature
(0,11) gives a bosonic E_11 that does not extend
to supersymmetry. Possibly, fundamnetal starting
point for Euclidean formulation of finite
temperature string/M theory.

7
Generalized Electric Magnetic Duality The
heterotic-type IA-type IB theories have the
generalized Poincare-Hodge duality of an 11d
theory, not necessarily with full 11d Poincare
invariance. Remarkably, we discover the elusive
spacetime evidence of the 12th member in the
Dbrane spectrum, magnetic dual to the D8brane, in
a worldsheet calculation, the unique extension
with modified Dirichlet boundary conditions to
Polchinskis Dpbrane tension calculation for p
-1, 0, 1, , 9. In 10d Hodge duality, we find
missing dual to the spacefilling D9brane 11d
Hodge duality is complete p (-2), (-1), 0, 1,
2, 3, and their 11d Hodge duals, 49. O. Alvarez
(82). Cohen, Moore, Nelson, Polchinski (86).
Chaudhuri, Chen, Novak, 1999. Douglas,
Kabat, Pouiliot, Shenker 1996. Chaudhuri Novak
0002046. Exact double expansion in external
field and distance was obtained, arbitrary field
strength. The earliest evidence of
sub-string-size monopoles, carry magnetic dual of
D8brane charge---End of an F-soliton string on an
D8brane, in external B field. Chaudhuri,
hep-th/0007056.Pointlike monopoles are the zero
size limit of a pair of circular line operators
on D8branes. Finite sized loops frame surface
operators (Framed BPS States, Gaiotto,
Nietzke,Moore, 10) Remark Compactification on
a circle gives a KK oneform, possible extension
to E_11.

8

• Matrix Theory and the Fundamental Symmetry
  
• A Planck Scale Generalized Electric Magnetic
  Dual Initial State
• A matrix realization of this algebra on a Planck
  sized bubble of spacetime is conjectured to be
  generalized EM selfdual Initial State Universe
  with the generalized electric magnetic self dual
  spectrum of 12 pforms.
• (Chaudhuri, 2004, 2008-10.)
• IV. Conclusions Conjectures and Future Work. In
  9d and below, and with 8 susy, 4 susy on K3 x T2,
  likely the algebra will extend to E_10, E_11.
  Needs an update, a systematic analysis,
  fascinating prospects, exciting new stage for
  String/M Theory!!
• (Open Questions in hep-th/0404235, Chaudhuri
  w/Lowe, 9512226 and w/ H. Verlinde.)

In 0201129, 0408057, I showed what modifications
of M(atrix Theory) and the IKKT IIB Matrix Model
were needed for a matrix realization of the
algebra large N is a flavor
symmetry, G_YM is finite rank, and (volume
preserving) Lorentx x Supersymmetry extends to
the full Electric-Magnetic Duality group D_11.
Spacetime Matter emergent.