Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model

G. Vernizzi (NBI); J. Nishimura

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Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model

J. Nishimura, G. Vernizzi (NBI)

High Energy Physics - Theory · Submitted 24 Mar 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one.

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We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter `nu' which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue that it is likely that the remaining eight-dimensional Lorentz invariance is further broken, which can be checked by integrating over the saddle-point configurations using standard Monte Carlo simulation.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter `nu' which couples to the imaginary part of the effective action induced by fermions.	contribution 0.72	0.86	0.04	asserted 0.55
s1	The deformed IIB matrix model continues to be well-defined for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and the cluster property.	result 0.84	0.52	0.06	asserted 1.00
s2	We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one.	result 0.97	0.96	0.82	asserted 0.97
s3	We argue that it is likely that the remaining eight-dimensional Lorentz invariance is further broken, which can be checked by integrating over the saddle-point configurations using standard Monte Carlo simulation.	future work 0.94	0.27	0.11	hedged possibility 0.99

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Original abstract

We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter `nu' which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue that it is likely that the remaining eight-dimensional Lorentz invariance is further broken, which can be checked by integrating over the saddle-point configurations using standard Monte Carlo simulation.

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References

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

An effective field theory approach to the sign problem in BFSS
hep-th 2026-06 unverdicted novelty 8.0 of 10

The Pfaffian phase in BFSS becomes an O(9) pseudoscalar operator in a bosonic matrix integral, requiring 10-loop order in the high-T expansion before the sign problem is detectable in the 't Hooft regime.
Emergence of a 4D World from Causal Quantum Gravity
hep-th 2004-04 conditional novelty 8.0 of 10

Monte Carlo simulations of four-dimensional causal dynamical triangulations yield an extended quantum geometry whose spatial slices have Hausdorff dimension 3.10 plus or minus 0.15 and whose volume scaling matches a c...
Pfaffian sensitivity to temporal deformations of an N=5 background in the Lorentzian IIB matrix model
hep-th 2026-11 conditional novelty 6.0 of 10

For an N=5 Lorentzian IIB matrix-model background, the one-loop Pfaffian gradient is concentrated in a two-plane fixed by the background geometry, and the classical spatial 3+6 hierarchy is modestly strengthened by co...
Regularized Master-Field Approximation for Mass-Deformed Supersymmetric Yang-Mills Matrix Models
hep-th 2026-10 conditional novelty 6.0 of 10

The regularized master-field approximation reproduces fuzzy-sphere phases in three mass-deformed supersymmetric matrix models, including the polarised IKKT model, and shows that Dirac zero modes can destabilize the sphere.
One-Loop Fluctuation Response Along a Constrained Noncommutative Modulus in the Lorentzian IIB Matrix Model
hep-th 2026-08 conditional novelty 5.0 of 10

On a constrained N=5 Lorentzian IIB branch with numerically constant quadratic extent spectrum, the fermionic Pfaffian and the framed higher-L SO(5) observables vary along the modulus and resolve the degeneracy.

Show 3 more citing papers

Late time behaviors of the expanding universe in the IIB matrix model
hep-th 2012-08 conditional novelty 5.0 of 10

A classical solution of the Lorentzian IIB matrix model gives a scale factor whose equation-of-state parameter drifts from -1 to -1/3, offered as a dynamical explanation for the smallness of the cosmological constant.
Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
hep-th 2011-08 conditional novelty 5.0 of 10

A systematic third-order Gaussian-expansion scan of all SO(d) symmetric vacua (2 <= d <= 7) of the type IIB matrix model finds the free energy minimized at d = 3, not d = 4, with a d-independent space-time volume for d >= 3.
Multi-Matrix Quantum Mechanics, Collective Fields and Emergent Space
hep-th 2026-05 unverdicted novelty 4.0 of 10

Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution.

How the literature uses it

16 arXiv papers cite this in 30 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 18 sentences without a confident label

Compares with it 1 paper

Taking into account the argument that an SO($2$) vacuum is not likely to be realized in this model [ref] , we conclude that our results are consistent with the ones obtained by using the GEM on the Euclidean IKKT matrix model [ref] , which predict SSB to an SO($3$) vacuum.

Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model · Summary and discussions · 0.95

Cites it as support 3 papers

This is based on the fact that the Pfaffian vanishes identically for strictly 2D configurations [ref] , which implies that the mechanism of SSB due to the phase of the Pfaffian no longer works there[This is also reflected in the GEM results [ref] for the free energy of the SO($d$) vacuum, which becomes much larger for $d=2$ than for $d≥3$.].

Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking · Results · 0.98
In Ref. [ref] it was shown that configurations with lower dimensions result in milder fluctuations of $Γ$, which points to the mechanism for favoring configurations less symmetric than SO($10$).

Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model · the Euclidean version · 0.98
It is actually the strong fluctuations of this complex phase that provide the mechanism for the dynamical compactification of space-time [ref] .

Progress in the numerical studies of the type IIB matrix model · Absence of the SSB without the complex phase · 0.96

Cites it as background 4 papers

Since the Pfaffian $Pf M(A)$ is real unlike in the Euclidean case [ref] , the model ([ref]) can be studied by Monte Carlo simulation without the sign problem.[Strictly speaking, the Pfaffian is not positive semi-definite.

A renormalization group method for studying the early universe in the Lorentzian IIB matrix model · Brief review of the Lorentzian IIB matrix model · 0.80
The space-time structure has been studied by various approaches in this Euclidean model [ref] .

Late time behaviors of the expanding universe in the IIB matrix model · The IIB matrix model and the birth of the universe · 0.99
Further discussion of the polynomial $𝒫_D, N[A]$ appears in Sec. [ref] and Refs. [ref] .

IIB matrix model, bosonic master field, and emergent spacetime · Critical-point setup: General case · 0.90

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