Saturday, July 7, 2018

On Flux Compactifications and Large Hierarchy

Flux Compactifications were introduced by Strominger  as well as De Wit, Smit and Hari Dass as a generalization of conventional Calabi-Yau Compactifications.

In his article Superstrings with Torsion published in Nucl. Phys. B274 (1986) 253 Strominger and on the other hand  de Wit, Smit and Hari Dass in their article Residual Supersymmetry for Compactified d=10 Supergravity introduced solutions of Killing equations where the metric included the warp factor and the torsion was non-zero.

This is simpler than it sounds.

General relativity equations give spacetime metrics as solutions.

The supergravity equations, the low energy effective theories corresponding string theories, demand at least two more field apart from the metric. These are the torsion and the dilaton. Plus there can be other bosonic fields apart from the fermionic ones.

So in case of the solutions that we are talking about the innovation is the presence of the torsion as well as the warp factor.

Because of the presence of the warp factor the metric is not a direct product of the internal and external factors when we start talking about compactifications.

Compactifications we have to talk about - after all superstrings prefer to live in ten dimensions while we are determined to live in four.

The fun part is that These new compactifications are generalizations of Calabi-Yau compactifications because these too give us supersymmetric solutions and these possess warp factors.

Of course there were no-go theorems that implied that most of these new compactifications would be equivalent to usual Calabi-Yau compactifications. Yet develoments in non-perturbative string theory and M-Theory suggested that these no-go theorems could be circumvented.

Hence were born the entities that we today call Flux compactifications.

Corresponding M-Theory and F-theory versions were found.

Then came Giddings, Kachru and Polchinski and told us that the flux compactifications can give large hierarchy of scales.

Now that is neat. I mean that is useful. we need hierarchy in physics to solve the hierarchy problem.


Thursday, July 5, 2018

The de Sitter Lore

(1) Witten gave a talk at Strings 2001 in Mumbai and the write up is available at the arXiv as [hep-th/0106109] with title 'Quantum Gravity in de Sitter Space'.

(2) In the same year we have an article by Tom Banks on Cosmological Breaking of Supersymmetry, IJMPA 19(2001)910.

(3) In October 2002 there was a paper by W Fischler, T. Banks and S. Paban on 'Recurring Nightmare : Measurement Theory in de Sitter Space' [hep-th/0210160]

(4) On December 19, 2002 J.Distler has a post on 'De Sitter on My Mind' on his blog Musings.

(5) On January 30, 2003 he has another post on the same blog called 'Long Live de Sitter'.

(6) On April 8, 2003 he has yet another post called 'For One, Many'.

(7) On February 4, 2017 J. Distler had one more post on his blog called Responsibility.

QED vs String Theory

Hirosi Ooguri wrote a comment on Shamit Kachru's wall that the difference between QED and string theory is that in QED the structure constant is an adjustable parameter.

In string scenario the choice of NS and R fluxes fix the hierarchy scales.

KKLT on de Sitter Vacua in String Theory

This is a string theory paper on cosmology that has been cited by 2532 papers till date (July 5, 2018). 

It was published in the Physical Review D in 2003 and the exact citation is Phys.Rev. D68 (2003) 046005. 

The authors are Shamit Kachru, Renata Kallosh, Andrei Linde and Sandip Trivedi.

The paper appeared on the arXiv as [hep-th/0301240].

It is about construction of meta-stable string vacua using highly warped Type IIB compactifications with both NS and RR non-trivial three form fluxes. 

Then using Euclidean D-instantons or gluino condensates AdS vaqua with stable moduli can be created.

Finally addition of anti-three branes in small amount lifts the vacua to meta-stable de Sitter vacua.

Then you can live in this universe for the duration that is larger than the life time of our cosmos.

See you need permission to live in your own universe. Authors assure us that the life time of the state will always be less than the recurrence time.

Polchinski wrote in the abstract of a review talk about these issues :

String theory has few or no stable non-supersymmetric or de Sitter vacua, only metastable ones. Anti-branes are a simple source of supersymmetry breaking, as in the KKLT model, but various arguments have been given that these fail to produce the desired vacua. Proper analysis of the system requires identifying the correct effective field theories at various scales. We find that it reproduces the KKLT conclusions.

That was in 2015.

In 2001 Giddings, Kachru and Polchinsti wrote in a paper's abstract :

Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory and F-theory compactifications on Calabi-Yau four-folds. In each case, the hierarchy of scales is fixed by a choice of RR and NS fluxes in the compact manifold. Our solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining N=1 supersymmetric gauge theory,and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.