Itzhak Bars- Phase Space Gauge Symmetry, 2T‐physics and its Predictions

8/3/2019 Itzhak Bars- Phase Space Gauge Symmetry, 2Tphysics and its Predictions

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Phase Space Gauge Symmetry, 2T h sics and its Predictions

Itzhak BarsUniversity of Southern California

ENS, XLme Institut dtJuillet 2010


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2T-Physics follows from a

.It leads to deep consequences for physics and

4+2 versions SM, Gravity, MSSM, GUTS, constructed.

-

Most recent: 10+2 SYM, 4+2 SUGRA,including NO SCALE MODELS as shadows in 3+1.

2T Works for LHC henomenolo , and

naturally 0 (or tiny) cosmological constant.

New physics guidance for 3+1, such as ideas for Higgs sector, Cosmology, Origin of GR Constant,

Absence of axion, Other possible origins of mass,

On technical side: A whole new set of hidden symmetries and dualities,with potential for developing new non-perturbative computational tools.

Recent paper,S. WeinbergGreens

functions in 4+2dims. obeying2T-physics..


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Strong hints for 2Tphysics came from Mtheory (IB 1995):

Extended SUSY

of

11D

M

theory

is

really

a

SUSY

in

12

dimensions

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{Q 32 ,Q 32}=(P+Z[2]+Z[5] )11D = (T[2]+T[6]+ )12DQ 32 spinor in 11D, also Weyl spinor 12D, real (10+2) signature!

consequences o eory a are exp a ne y on y s extended SUSY automatically have a 10+2 interpretation.

Soon after, more clues for 2T developed in F theory , S theory,

If this really implies 2 times, what is the dynamics, and how does one remove the ghosts?

2Tphysics developed by finding the fundamental solution to the

g os pro em , re a e causa y pro em , pr nc p e or ynam cs .

M , MEmerged from earlier ideas on 2T by IB + Kounnas (1997) (two particles, P1M,P2M)

This is independent of Mtheory, but I think will eventually explain (M)Stheory, with OSp(1|64) SUSY


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The Fundamental Principle (1998)4/26

General coordinate invariance removes bias

pos on-momen um symme ry n e ormu a on o un amen a p ys cs

of observers in Xspace (Einstein).

(XM

,PM), not just in Xspace. Hints: Poisson brackets, quan um commu a ors, ua es n eory e ec r c magne c

Implement this with a subset of canonical

transformations localized on the worldline .

symmetry.


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5/26Three generators Q ij(X,P): {Q 11 , Q 22 , Q 12=Q 21}Sp(2,R)

gauge,

Example, flat spacetime:

symme ry

11= . ,

22= . ,

12= . , any signature metric.

ij , expand in powers of P M, coefficients = e sc.t. generate general coordinate symmetry, gauge symmetry, and much more symmetry (hep-th/0103042).

gaugesymmetry.Local in

auge nvar an sec or ij= .It exists non-trivially only if spacetime has two times ,

no less and no moreAij( ) is Sp(2,R) gauge potential

xamp e: sp n ess par c e reparametrization

which requires 1T


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X ( ) X + ( ) X ( ) Make 2 gauge

choices.

Solve

2

P ( )P+ ( ) P ( )constraints. Remains 1 gauge choice and 1 constraint

Mass : modulus in the embedding of d dimensional phase space into d+2.

curvature

Time and Hamiltonian are different in each case < > 1T perspectives in

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. . gauge invariant relations among them . (info absent in 1T physics)

Any function of L MN =X M P N -X N P M is gauge invariant.


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7/26 X 0 X 0 X 1 X i


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MasslessShadows from 2T physics hidden info in 1T physics

Free or interacting Hidden Symm.

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particle ( p )

2=0 conformal sym

Dirac

systems with/withoutmass in flat/curved 3+1 space time

SO(d,2), (d=4) C2=1-d 2/4 = - 3

singleton

Massive

Emergent spacetimes

and emergent 2Tphysicstime & Hamiltonian in 3+1 attributed

relativistic ( p )

2+m 2=0

Non relativistic

armon c oscillator

2 space dims mass = 3rd dim

parameters: mass,

couplings, curvature, etc .

p , gauge symm. generators Q ij(X,P) vanish

simplest example X2=P2=X P=0 gauge inv.

to perspectives of observers in 4+2 phase space

H=p 2/2m, x

2Tphysics predicts Main points

1) no ghosts:

space: flat 4+2 dimsSO(4,2) symmetry

Hatom 3 space dimsH=p 2/2m a/r

en symmetr es and dualities (with parameters) among the shadows

p ys cs s compatible with 1Tphysics

2) Systematic new x

SO(3)xSO(1,2) info & insight

absent

in

1T physicsShadows emerge for choices of the Q ij(X,P) & in 2T field theory


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2T Field Theory, including interactions.9/26

Physical states Q ij(X, ) (X)=0 field eoms.

W at is

t e

action

princip e

t at

generates

t ese

as equations of motion through the variationalprinciple?

BRST field theory, IB+Y.C.Kuo 0605267, like string field theory Integrate out ghosts and other redundants ,

, , ,

,has its own new gauge symmetries, eliminate all

, .

Relation to 1T field theory 1T field th. shadows.


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The

relation

between

2T

physics

and

2T Physics as a completion and unifying framework for 1T physics10/26

Observers like us

1T physics described by an analogy : Consider object in the room

(phase space, XM,PM in 4+2 dims.)

are stuck on the walls (3+1 dims.), no privilege to be in the room 4+2 .

and

its

MANY

shadows

on

walls

(MANY phase spaces, xm ,p m in 3+1 ) xm ,p m

holo ra hic

ONE 2T system MANY 1T systemsPredict many relations among the

shadows

(dualities,

symmetries

d+2).

XM,PM

Contains systematically missed information in 1T physics approach.

T is

in o

re ate

to

ig er

spacetime:

Instead of interpreting the shadows as different dynamical systems (1T), must reco nize the are ers ectives

xm

,p m

1) 1T physics is incomplete !!!in higher spacetime. Then, we can

indirectly see

the

extra

1+1

dims.

2) 2T physics makes new

testable predictions.


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Gravity as background in 2Tphysics 0804.1585 [hep th]

Compare to a case

Sp(2,R) algebra puts kinematic constraints on fields

, impose Q 11=Q 12=0:

One of the shadows, conformal shadow .


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Gravity & SM in 2Tphysics Field TheoryIB: 0804.1585 IB+S.H.Chen0811.2510

Gauge symmetry and consistency with Sp(2,R) lead to a unique gravity action in d+2 dims, with no parameters at all .

Pure gravity has three fields:GMN(X), metric , aton

W(X), appears in (W) , and

No scale,

The equations of motion reproduce the Sp(2,R) constraints,called kinematic e uations ro ortional to W W and also the dynamical equations (proportional to (W)).


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2T Gravity triplet has unique couplings to matter: scalars, spinors & vectors.mposes severe constra nts on sca ar e s coup e to grav ty.


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components from vectors, tensors & spinors,

M .

e. . A X M A x , etc.shadows!

ot a uza- e n.

In particular the Standard Model works perfectly, So, SM is a 2T theory in 6D, after all !!


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15/26Gravitational scale (and other scales),

Conformal shadow : All shadow scalars as conformal scalars

Local scale symm ( x) comes from general coordinate symm in d+2. , . .

Gravitational scale . Good thing because the would be massless dilaton is a negative norm ghost

vacuum values of all scalar fields. It increases after every cosmic phase transition at the scales of inflation, GUT, SUSY, electroweak. Effect on cosmology !!

Furthermore, the SM is conformally invariant at the classical level:SO(4,2) in 6D takes the form of conformal transformations in 4D !!

No mass for Higgs, instead it develops from V= (H*H-2 2)2 , more physical !!


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2T SUGRA in d+2 dimensions 16/26

Gravity in 2T has no dimensionful constant. Newtons constant emerges from vacuum value of the Dilaton.

Therefore expect the same from SUGRA in d+2.s s a o w s a supersymme r ze orm o compensa or e p us ma er, e c.

Is there such a thing?? YES ! Shadow of 6D leads to NO SCALE MODELS in 4D! , , ,

Thanks Ferrara, Kounnas for pointing out the old work, and No Scale Models.

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s roa w ea o n an vers on o eoryExpect to produce a dynamical basis for earlier work on algebraic Stheory in 11+2

(hep th/ 9607112, 9608061), Mtheory type dualities, etc. (see hep th/9904063)


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N=1, 4+2

SUGRA

Gravity : e a , , b , z=s+ip4D

conformalcoupledto chiral

multiplets

. , , , ,,shadow.

There is a Weyl symmetry that emerges as a remnant.

There is also a local U(1), part of local SU(2,2|1). 0 plays the role of a complex compensator.

More general

homogeneous of degree 3


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NO SCALE:a superpotentialindependent of +

simplepotential

vanishes atminimum zerocosmologicalconstant c ass ca


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Super Yang Mills in 10+2 dimensions 19/26

Previous work: General SUSY Field Theory, for N=1,2,4, in 4+2 dimensions IB + YC.Kuo hep th/ 0702089, 0703002, 0808.0537

Usual N=4 SYM in d=4 is the conformal shadow from 4+2

12D theory

Note G,W, general gravity background

Homothety: Lie derivativeobey Sp(2,R) constraints


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For most background geometries such (X) can be found with only

But there are special cases with 32 components. For example, dimensionally reduce 10+2 to (4+2)+(6+0), then we obtain 32 component

16 independent components. , which in turn has N=4 SYM in 3+1 dimensions in

the conformal shadow.


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10+2 SYM as parent of N=4 SYM in 3+1, and a web of dualities 22/26

N=1 SYM in 10+2

SUSY condition on 32 spinor

u y compactifiedtheory = M(atrix) theory.

Compactify 6D : Conformal shadow: More 9+1 shadows, = 32 SUSYs

=

16 SUSYsand other compactifications to

d+2, with 1


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23/26Progress in 2Tphysics Local Sp(2,R): A general principle in Class. & Quant. Mech.

A principle for a higher unification and deeper insight into physics & space-timeReveals more physics phenomena that are systematically missed in 1T-physics.

With SUGRAThe Standard Model, General Relativity, and GUTS in 2T-physics,IB+Y.C.Kuo 0605267 , IB 0606045, 0610187, 0804.1585; IB+S.H.Chen 0811.2510Phenomenological applications: Cosmology 1004.0752 , LHC 0606045, 0610187 , and in progressPath inte ral uantization in d+2 field theor in ro ress

SU(2,2|1) givesno scale models0 cosm. const.,

SUSY in 4+2 and in Higher dimensionsIB+Y.C.Kuo, 0702089, 0703002, 0808.0537 (N=1,2,4 in 4+2 dims) Klein-Gordon, Dirac, Yang-Mills fields.IB+Y.C.Kuo , N=1 SYM in 10+2 (parent of N=4 SYM in 3+1; parent of M(atrix) theory).

...

- , .


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24/26Progress in 2Tphysics Local Sp(2,R): A general principle in Class. & Quant. Mech.

A principle for a higher unification and deeper insight into physics & space-timeReveals more physics phenomena that are systematically missed in 1T-physics.

Reminiscent of

The Standard Model, General Relativity, and GUTS in 2T-physics,IB+Y.C.Kuo 0605267 , IB 0606045, 0610187, 0804.1585; IB+S.H.Chen 0811.2510Phenomenological applications: Cosmology 1004.0752 , LHC 0606045, 0610187 , and in progressPath inte ral uantization in d+2 field theor in ro ress

a subset of no

scale models,0 cosm. const.,

SUSY in 4+2 and in Higher dimensionsIB+Y.C.Kuo, 0702089, 0703002, 0808.0537 (N=1,2,4 in 4+2 dims) Klein-Gordon, Dirac, Yang-Mills fields.IB+Y.C.Kuo , N=1 SYM in 10+2 (parent of N=4 SYM in 3+1; parent of M(atrix) theory).

...

- , .

Strings, Branes, M-theory in 2T-physics (partial progress)IB+Deliduman+Minic, 9906223, 9904063 ( tensionless string ); IB 0407239 ( twistor string )M-theory ; expect 11+2 dims OSp(1|64) global SUSY, related to S-theory (IB 9607112)

Non-perturbative technical tools in 1T-field theorySp(2,R)-induced dualities among 1T field theories (many shadows of 2T-field theory)IB+Chen+Quelin 0705.2834; IB+Quelin 0802.1947 + in progress. Note: S. Weinberg 1006.3480.

A more fundamental approach field theory in phase space (full Q,P symm)IB + Deliduman 0103042, IB + S.J.Rey 0104135, IB 0106013, + under development.


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All this is based on a provisional 25/26

form of 2T field theory.

Expect a more fundamental form of field theory in phase space which

, redicts more partially developed

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. . , ,

+ under development


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Where to find more information26/26

on -p ys csFor concepts and technical guidance on over 50 papers

.

A book at an elementary level for science enthusiasts (Springer 2009):

ByItzhak Bars

andJohn Terning

It can be downloaded at your university if your library has a

contract with Springer

26

. .DOI: 10.1007/978-0-387-77638-5

Itzhak Bars- Phase Space Gauge Symmetry, 2T‐physics and its Predictions

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