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A String Manifesto
Marcus BergCoPS
Open Office (Linux)
M.B., Haack, Pajer '07M.B., Haack, Körs '05, '04
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A String Manifesto
Marcus BergCoPS
● Summary of current state of affairs ● Statement about future plans ● Based on opinion (but strongly held)● Aim for future influence
Open Office (Linux)
Talk posted on website cops.physto.se/~mberg
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Outline
● Selective history of string theory
● Current research in string theory (very brief)
● Current research in string phenomenology
● My research on “KKLTlike orientifolds”
● Future directions / points of contact
details: VRfoass lecture series!
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Selective history of string theory
1968 Veneziano
19681973 Early history“The Birth of String Theory”, miniconferenceGGI Florence, May 1819 2007http://theory.fi.infn.it/colomo/stringbirth/
1980s Early exploration of string perturbation theory: thermodynamics, ultrahigh energy, heavy states Ex: Sundborg thesis: “Strings Hot Fast and Heavy”
Early attempts at phenomenology Ex: “Rank of gauge group must be < 23” (... or not)
(see intro to Kachru, McGreevy, Svrcek '06)
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1980s Orientifold models, “halfSUSY” (not much attention)(cont'd) Strong statements
1990s Early explorations of nonperturbative string theory Dualities DBranes AdS/CFT
Even stronger statements
2000s Putting things together: more general backgrounds Ex. “strongly timedependent backgrounds” (promising for cosmological models)
Less strong statements (still occasionally outrageous)
Selective history of string theorySagnotti '87, ...
..., Polchinski '95
..., Maldacena '97
Balasubramanian, Hassan et al '02
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Current research in string theory
N=2, N=4, N=8N=1N=0
Amount of supersymmetry
AdS/QCD“Applied AdS/CFT”
String phenoString cosmo
KKLT
Heterotic modelsSasakiEinstein/Quivers
SQCD in AdS/CFTString instantons
Intersecting branes/MSSMNongeometric backgrounds
Supergravity solutionsTopological strings
Mtheory / Matrix modelsTopological Mtheory
Spin chains
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String Phenomenology I: Soft Supersymmetry Breaking
D=4, N=1 effective quantum field theory (supergravity)
Kähler potential K, superpotential W, gauge kinetic function f ...
break supersymmetry spontaneously:
particle physics
cosmology
“hidden sector” = “moduli”
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String Phenomenology II: Low Energy Spectrum
Example: LVS (dilute flux, C)
SoftSUSY
future discussions
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String Phenomenology III: LHC observables
PYTHIA PGS
Kane, Kumar, Shao '06Conlon, Kom, Suruliz, Allanach, Quevedo '07
How sure are we about these 'clouds'?
future discussions
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String Cosmology I: Soft Supersymmetry Breaking
D=4, N=1 effective supergravity
Kähler potential K, superpotential W, gauge kinetic function f ...
break supersymmetry spontaneously:
particle
cosmology
Inflaton one of these
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String Cosmology II: Dark energy
(not much more later)
● Some ideas● None really attractive● In the following, will parameterize, not explain
future discussions
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String Cosmology III: Inflation
Generic “moduli”: denote by
Observable parameters: computable analytical functions of moduli(though difficult)
(more later)
Sep 2007
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“stringinspired scenarios”
?
hep
th
hep
phString Phenomenology: Pessimism vs. Optimism
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String Phenomenology: Pessimism vs. Optimism
“stringinspired scenarios”
“match to experiment”
Go on to matchmore experimental data
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“stringinspired scenarios”
INCONSISTENCY(examples later)
Supersymmetry breaking?Instability? (any direction in moduli space!)Higherderivative / quantum corrections?Nonperturbative effects?
?
Montparnasse 1895
String Phenomenology: Pessimism vs. Optimism
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Oldfashioned compactification
Candelas, Horowitz, Strominger, Witten '85...
4D Minkowski space CalabiYau manifold (N=1 SUSY)
Topological properties rough phenomenology in 4D
Candelas, de la Ossa, He, Szendroi '07
here: code for “concrete model”
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Some issues with oldfashioned compactifications
● Tend to lose control when supersymmetry is broken
● The moduli problem: no “stabilization” (Want potential energy for moduli, but supersymmetry prevents it) ... maybe we can ignore this? (later)
● No cosmological constant
● Usually only “rough” phenomenology (need details to address e.g. flavor problem)
● No known CalabiYau metric! (only topological information)
● Explicit models can be ruled out! (if taken literally) (Ex. quintic gives 100 visible generations)
Uniqueness?
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Warped compactification with Dbranes
Kachru, Kallosh, Linde, Trivedi '03Giddings, Kachru, Polchinski '01
deSitter Topology stabilization (vacuum selection)
Curvature dynamics (e.g. inflation)
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The KKLT 6D internal space:
a CalabiYau orientifold with fluxes and warping
Kachru, Kallosh, Linde, Trivedi '03Giddings, Kachru, Polchinski '01
Topology
stabilization (vacuum selection) – more explicit a few slides later
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The KKLT 6D internal space:
a CalabiYau orientifold with fluxes and warping
Kachru, Kallosh, Linde, Trivedi '03Giddings, Kachru, Polchinski '01
“warped throats” (originally conceivedas RandallSundrum type scenarios)but: RS was 1D, this is 6D
Explicit “warped throat” noncompact 6D CalabiYau metric!Can consider dynamics in extra dimensions, e.g. Dbrane inflation.
Klebanov, Strassler '00
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The KKLT 6D internal space:
a CalabiYau orientifold with fluxes and warping
Kachru, Kallosh, Linde, Trivedi '03Giddings, Kachru, Polchinski '01
“warped throats” (originally conceivedas RandallSundrum type scenarios)but: RS was 1D, this is 6D
Simplest approximation to “warped throat”: D3brane moving in AdS . 5
Kachru, Kallosh, Linde, Maldacena, McAllister, Trivedi '03
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Effective quantum field theory from string theory
“Old” string perturbation theory: very rigid double expansion
● E expansion (energy vs. string length) “all or nothing!”● (string coupling) expansion = loop expansion● String length ~ Planck scale● GUT unification
“New” string perturbation theory: more flexible
● N flux quanta – new parameter (labels vacua)● N number of Dbranes – new parameter (cf. 1/N expansion)● Include some nonperturbative effects (estimates, e.g. A)● String length only restricted by phenomenology● Often nonstandard gauge unification
FD
eg. Giddings, Kachru, Polchinski '01
(many exceptions and caveats here)
eg. GreenSchwartzWitten
In both cases, can only rarely truncate perturbation theory (but only then is it really interesting)
2
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KKLT D=4, N=1 effective theory: vacuum selection
Stabilize S and U(i.e. minimize potential Vwith respect to S and U)
Now stabilize Kähler moduli T
Moduli from earlier : break up into S, T, U
6D overall volume
as function of parameters T
(“Kähler moduli”)
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Stabilize Kähler moduli in KKLT
For K given on previous slide (leading order), it so happens that
so potential vanishes, T is not stabilized (“noscale model”)
Beyond leading order: broken by all kinds of correctionsIn KKLT, by nonperturbative corrections to W
Details: e.g appendix of M.B., Haack, Pajer '07
Cremmer, Ferrara, Kounnas, Nanopoulos '83
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Stabilize Kähler moduli in KKLT
Beyond leading order: broken by all kinds of correctionsIn KKLT, by nonperturbative corrections to W
Point: In KKLT, all moduli are stabilized.This also means parameters in the effective theoryare all connected. We will see an example of this.
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Technical work left to compute
KKLT effective action parameters from string theory
● RamondRamond fluxes in string perturbation theory
● Supersymmetry breaking in string theory
● Nonperturbative superpotentials
● “Uplift” details (scale of inflation? dark energy?)
● Putting it all together
many different issues,
e.g. “tadpole problem”
Truly “topdown” approach
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One lesson made explicit by KKLT program
Moduli stabilization is not an afterthought! (“add later...”)
Example: compute soft supersymmetry breaking terms M, m, A, ... from flux superpotential alone
stabilize T restores supersymmetry!(M, m, A, ... = 0 )
String phenomenology needs moduli stabilization
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Some drawbacks with original KKLT
● only works for limited range of a, W, A
● volume not stabilized big (not really a “problem”, but see later)
● supersymmetry breaking “at the end” (least understood part)
● “twostep stabilization” sometimes fails (i.e. not algorithmic)
balanceto stabilize
real part of Kähler moduli
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The “LargeVolume Scenario” (LVS)
Truncation problem: it typically makes no sense to attempt to“improve” any leadingorder string model by string/quantum corrections
LVS is one case where this intuition may fail (under investigation!)
Balasubramanian, Berglund, Conlon, Quevedo '05Conlon, Quevedo, Suruliz '05
(higherderivative correction)
special CalabiYau
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LVS Kähler moduli stabilization
change variables:
dial volume!
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Why ?
● (inverse volume) expansion under control
● “twostep” integrating out becomes algorithmic
● matter fields:
● soft supersymmetry breaking terms: simplifications
Why is big good?Conlon, Quevedo, Suruliz '05
Why ? ● TeV supersymmetry
● QCD axion (strong CP problem)
● neutrino masses conn
ecti
ons
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Sample calculation: Gaugino Masses From LVS
Assume MSSM
Gaugino masses suppressed by ~ 30 compared to gravitino mass.
Conlon, Abdussalam, Quevedo, Suruliz '06
“Mirror mediation”
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“Mirror Mediation” in LVS
Conlon '07 (Oct 9)
● Flavor structure from only one kind of modulus (here U)
mass threshold
● New nonrenormalizable couplings at each mass threshold M (typical)
● Hard to compute f(U), but not unthinkable
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Conlon, Quevedo '07
LVS and dark matter?
● compute leadingorder couplings, masses and lifetimes
LVS = very practical, explicit model. Too good to be true?
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Consistency Conditions:
String Length vs. DBrane Loop Corrections
dimensional analysis:
Cancellation in scalar potential (to be shown):
should consider Dbrane corrections in LVS!
ignored in LVS
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DBrane Corrections to Kähler potentialM.B., Haack, Körs '05
s=2 case of
Dbrane (where open stringscan end)
Orientifold plane(fixed plane of worldsheet parity operation)
Final answer:
Toroidal orientifold(much simpler than LVS)
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Demystifying generalized holomorphic Eisenstein series
(This is f(U) that appears in loop correction to Kähler potential)
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Integrate loopcorrected Kähler metric to get Kähler potential
“Kähler puzzle”: OK for T, but what about the D3brane scalar,is this consistent with D7brane gauge coupling loop corrections?
In other words, we are integrating a PDE – are the integrability conditions due to other loop corrections satisfied? (Answer at the end)
this is what we did onprevious 2 slides
for experts:
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Generalizing to LVS (here: contribution from KK states)
Based on results in toroidal orientifolds,guess the important aspects of results in LVS
(obviously, much work left to do here!)
M.B., Haack, Pajer '07
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LVS + Loop Corrections (specific model)
● Some magical cancellations (“extended noscale”)
● Can now minimize full, corrected potential
● Perturbative term depends on more moduli now
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Scalar Potential V with String Loop Corrections
For this type of CalabiYau, loop corrections can be neglected (in V)
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Ex: loopcorrected nonperturbative superpotentialGeneralization to KKLT, LVS?
Gauge coupling correction ~ potential for D3brane scalars (inflaton)
M.B., Haack, Körs '04Giddings, Maharana '05
Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan '06
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Realization: this is also the scalar propagator on a 2torustransverse to the D7branes!
“Green's function method”:integrate propagator over 4cycle wrapped by D7branes,was applied to warped throat metrics(curiously: AdS/CFT intuition useful!)
Generalization to KKLT, LVS?Ex: loopcorrected nonperturbative superpotential
M.B., Haack, Körs '04Giddings, Maharana '05
Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan '06
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D3brane potentials:
MSSM flavor structure <> inflaton potential?
Dependence on
“N=2”
“Inflation
potential” (IPI)
Relate particle physics (e.g. gaugino masses) and cosmology (e.g. inflation)!
Many technical aspects to be sorted out... (e.g. twisted strings)
Baumann, Dymarsky, Klebanov, McAllister '07Krause, Pajer '07
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Inflection point inflation
..., Itzhaki, Kovetz '07 (Aug)
Work in progress – but shows one aspect of string models:maybe not unique, but very restrictive!
In the only class of models where the D3brane potential is currently known, the inflaton is massless!
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Resolution of Kähler puzzle
(gauge coupling vs. Kähler metric integrability)
Fits with gauge coupling corrections
M.B., Haack, Körs '05
for experts:
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Summary
● Much work left to achieve safe and interesting stabilized models
● LVS is promising: LHC phenomenology, dark matter, etc.
● Our LVS consistency check (“jumping through loops”) OK
● LVS won't work for generic (?) CalabiYaus but maybe cousin?
● Dbrane inflation: progress on computing potentials
(work in progress w. M. Haack)
details: VRfoass lecture series!
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Future directions
● Instead of LVS: purely perturbative stabilization?
● “Bottomup”: Effective action analysis: BMSSM
● “Topdown”:Further study of effective action as function of moduli
● “Green function method”? Much more general models
● DBrane inflation: IPI, what next?
● Inflation and the renormalization group?
● Strong time dependence?
● Dark energy models? (Journal club w. S. Hofmann at Nordita)
M.B., Haack, Körs '05
Dine, Seiberg, Thomas '07
Hertzberg, Tegmark, Kachru et al '07
(w. M. Haack)
details: VRfoass lecture series!
cf. Balasubramanian, Hassan et al '02