Dynamical symmetry breaking
in nonperturbative string theory
Tsunehide Kuroki(Division of String Theory and Mathematics, KMI)
@KMI Topics, 2013/7/10

String theory as quantum gravity
Fundamental requirements of string theory: quantum gravity:
 consistent quantum (field) theory determines space-time itself
 reduced to the Einstein gravity→ four-dimensional Minkowski space(including its signature?),standard model of universe
 unified theory: standard model of particle physics

Perturbative string as a candidate
 includes both gauge boson (open string),

and graviton (closed string) (perturbatively) consistent quantum
theory nonrenormalizability of gravity→ extended object↓(almost) unique ultimate theory
respecting quantum theory(not Einstein gravity)

Virtues of perturbative string
essence: local scale invariance on WS st-duality
 UV-finiteness perturbative QG

 graviton in the spectrum (cf. QCD string) unification of external field & spectrum

 desirable as unified theory

Faults of perturbative string
 local scale invariance background EOM (Einstein eq.)

→ essentially perturbation theoryon-shell (1st quantization)
 anomaly → ten dimensions (critical dim.) infinite # of perturbative vacua

 serious as quantum gravity→ nonpert. formulation:
abandon local scale inv, even WS picture!

Nonpert. effect seen by
perturbative string large order behavior

cf. field theory:suggests nonpert. effectin spite of closed SFT action

cf.

[Shenker 1991]

D-branes as nonpert. effect (1) classical solution of closed SFT (soliton)
 black brane solution at low energy
 Dirichlet b.c. for open string st-duality→ source of closed stringD-branes as nonpert. effect (2) dynamics: open string oscillation[Polchinski 1995]

 action: open string disk amplitude tension result of st-duality:

large order behavior, nonpert. effect.:reflects difference from particle theory

Toward nonpert. formulation
 nonpert. effect does not always suggest

nonpert. formulation itself(D-brane: within perturbation theory) existence of D-particle, D-instanton “quantization” of soliton
 tractable thanks to st-duality:(a kind of) gauge theory (not BH dynamics)
 string duality:

F-string ⇔ D-brane (as SG ⇔ MT)in some string theory,
condensation of string ～ D-brane[花早石川黒松多 2004]

Candidates so far
 discretization of WS → matrix model

critical pt.: + large- lim. (double scaling lim.)→ smooth surface ( : technical tool for WS) D-brane matrix model:
Yang-Mills type gauge theory (target sp. pic.): gauge field on brane,: position

Virtues & faults: WS discretization
 virtues

 reproduce all order perturbation theory
 nonpert. effect ～ eigenvalue at saddle～ tunneling of eigenvalue→ WS boundary
nonpert. exact free energy (Painlevé eq.) faults

 available only in no space-time SUSY(noncritical string)Virtues & faults: D-brane matrix model virtues

 captures D-brane dynamics (@ low energy)
many examples:force, scattering, decay, recombination…
 concrete example as (classical) gravity:
AdS/CFT: region where closed string canbe described by gauge theory (st-duality) target sp. symm. (sometimes nontrivially) faults

 F-string DOF, scattering amp., st-duality

Why D-brane MM can contain gravity
D-brane MM ← quantization of massless
open string DOF → should be valid only
for D-brane dynamics @ low energy
far from full nonpert. closed string theorye.g.
IIB matrix model … D(-1)-brane (0d) [IKKT 1997]
Matrix theory … D0-brane (1d MQM) [BFSS 1997]
Matrix string th. … D-string (2d SYM) [DVV 1997]
AdS/CFT (strongest) … D3-brane (4d SYM)
[Maldacena 1998]

Key: symmetries (1) SUSYe.g. IIBMM
 maximal SUSY: graviton multiplet
 “emergent” 10d gravity(remnant of st-duality)

one-loop in gauge th. in background →Key: symmetries (2) isometry & conformal symmetry AdS5/CFT4: SO(4,2)
 other symm. ((broken) chiral symm. …)→ ensure validity low energy effectiveaction (w/ small # of parameters)(Note: even if symmetries do not agree,some quantities can be well describedby their peculiarity (universality, BPS, …))
usually, only very special closed string
can be reproduced …

(Maybe) Promising candidates
 IIBMM D(-1)-brane low energy effective action
 WS formulation of Schild gauge

0-dim. SYM can be regarded as D(-1)-brane low energy effective action
 matrix reg. of F-string in Schild gaugematrix reloaded[McGreevy Verlinde 2003]

 MQM: WS discretizationofstring LEEE of unstable D0-branearXiv:hep-th/0304224v3 22 Dec 2003

PUPT-2083
hep-th/0304224

Strings from Tachyons:
The c = 1 Matrix Reloaded

John McGreevy and Herman Verlinde

Department of Physics, Princeton University, Princeton, NJ 08544

Abstract
We propose a new interpretation of the c = 1 matrix model as the world-line theory of N unstable
D-particles, in which the hermitian matrix is provided by the non-abelian open string tachyon.
For D-branes in 1+1-d string theory, we find a direct quantitative match between the closed
string emission due to a rolling tachyon and that due to a rolling eigenvalue in the matrix model.
We explain the origin of the double-scaling limit, and interpret it as an extreme representativeof a large equivalence class of dual theories. Finally, we define a concrete decoupling limit ofunstable D-particles in IIB string theory that reduces to the c = 1 matrix model, suggesting that
1+1-d string theory represents the near-horizon limit of an ultra-dense gas of IIB D-particles.

Should perturbative string be realized?
 D-brane MMs (SYMs): difficult to reproduce

pert. string amplitude→ they must realize F-string, st-duality?
they should contain 10d gravity?
recall def. of quantum gravity:well-defined quantum th. + 4-dim. EH @ LE
(cf. LGT: allows weak coupling exp.)
desirable:
-expansion = perturbative exp. of F-string double scaling limit = nonperturbative string theory(cf. noncritical string) SUSY DW MM ← new e.g. of “desirable” oneDynamical symmetry breaking
in nonpert. string theory
 in “desirable” scenario,

-expansion: perturbative (w.r.t. ) exp.
symm. (in particular SUSY) is inevitable double scaling limit: nonpert. string theory→ two standard models @ LE
→ no symmetries!

MM or SYM withsymm. preserved @ all orders in
but gets broken in the DSL-exp.

Examples of DSB (1) rotational symm. in IIBMM: 0-dim. SYM

manifest SO(10) symm.
eigenvalues of: space-time pts→ originally 10-dim. flat sp.
 mean field approx.
[Nishimura Sugino 2001](adding)[川河黒松篠 2002][Kawai Aoyama 2006] etc.

→: 10 eigenvalues→ four-dim. space “emerges” dynamically

Example of DSB (2) SUSY DW MM:[T.K. Sugino 2013][Endres T.K. Sugino Suzuki]

w/ nilpotent SUSY’s
we have recently shown that:
 inthis MM reproduces several
types of tree level two-point functionsof 2D type IIA superstring theory: reproduce
perturbative string (although in 0-dim.!) SUSY’s are broken in the DSL via
an isolated eigenvalue asVirtues & faults of our model virtues

 reproduces tree level string amplitude→ expected st-duality
 SUSY is preserved at all orders in-exp.
 first e.g. of dynamical & nonperturbative
breaking of SUSY in string theory
 faults

 loses both WS picture & D-brane picture
 poor target space and fields
breaking of nilpotent SUSY is significant?