We propose a simple geometric interpretation for gauge/gravity duality, that relates the large-$N$ limit of gauge theory to the second quantization of string theory.
U($N$) supersymmetric Yang-Mills theory naturally appears as the low-energy effective theory of a system of $N$ D-branes and open strings between them. Transverse spatial directions emerge from scalar fields, which are $Ntimes N$ matrices with color
indices; roughly speaking, the eigenvalues are the locations of D-branes. In the past, it was argued that this simple emergent space picture cannot be used in the context of gauge/gravity duality, because the ground-state wave function delocalizes at large $N$, leading to a conflict with the locality in the bulk geometry. In this paper we show that this conventional wisdom is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. This conclusion is obtained by clarifying the meaning of the diagonalization of a matrix in Yang-Mills theory, which is not as obvious as one might think. This observation opens up the prospect of characterizing the bulk geometry via the color degrees of freedom in Yang-Mills theory, all the way down to the center of the bulk.
We propose a new framework for simulating $text{U}(k)$ Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to supersymmetric gauge t
heories. Our proposed approach yields a novel perspective on quantum simulation of quantum field theories, carrying certain advantages over the usual Kogut-Susskind formulation. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories, from glueball measurements to AdS/CFT, making use of a variety of quantum information techniques including qubitization, quantum signal processing, Jordan-Lee-Preskill bounds, and shadow tomography. The generalizations to certain supersymmetric Yang-Mills theories appear to be straightforward, providing a path towards the quantum simulation of quantum gravity via holographic duality.
We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain
states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. Our prescription consists of four steps: regularization of the Hilbert space, adiabatic state preparation, simulation of real-time dynamics, and measurements. Regularization is performed for the BMN matrix model with the introduction of energy cut-off via the truncation in the Fock space. We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state. Then, we provide an explicit construction for simulating real-time dynamics utilizing techniques of block-encoding, qubitization, and quantum signal processing. Lastly, we present a set of measurements and experiments that can be carried out on a quantum computer to further our understanding of superstring/M-theory beyond analytic results.
We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from $N^
0$ to $N^2$, which persists in the weak coupling region. Indistinguishability associated with the symmetry group -- SU($N$) or O($N$) in gauge theory, and S$_N$ permutations in the system of identical bosons -- is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite $N$, and for quantum gravity via gauge/gravity duality.
We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings mak
e the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-$q$ limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.
We provide the evidence for the existence of partially deconfined phase in large-$N$ gauge theory. In this phase, the SU($M$) subgroup of SU($N$) gauge group deconfines, where $frac{M}{N}$ changes continuously from zero (confined phase) to one (decon
fined phase). The partially deconfined phase may exist in real QCD with $N=3$.
We demonstrate a novel feature of certain phase transitions in theories with large rank symmetry group that exhibit specific types of non-local interactions. A typical example of such a theory is a large-$N$ gauge theory where by `non-local interacti
on we mean the all-to-all coupling of color degrees of freedom. Recently it has been pointed out that nontrivial features of the confinement/deconfinement transition are understood as consequences of the coexistence of the confined and deconfined phases on the group manifold describing the color degrees of freedom. While these novel features of the confinement/deconfinement transition are analogous to the two-phase coexistence at the first order transition of more familiar local theories, various differences such as the partial breaking of the symmetry group appear due to the non-local interaction. In this article, we show that similar phase transitions with partially broken symmetry can exist in various examples from QFT and string theory. Our examples include the deconfinement and chiral transition in QCD, Gross-Witten-Wadia transition in two-dimensional lattice gauge theory, Douglas-Kazakov transition in two-dimensional gauge theory on sphere, and black hole/black string transition.
We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU($N$) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and t
his hinders progress in understanding the nature of the black hole/black string topology change from the gauge/gravity duality perspective. On the one hand, previous works considered the deconfinement transition consistent with two transitions which are of second and third order. On the other hand, evidence for a first order transition was put forward more recently. We perform high-statistics lattice Monte Carlo simulations at large $N$ and small lattice spacing to establish that the transition is really of first order. Our findings flag a warning that the required large-$N$ and continuum limit might not have been reached in earlier publications, and that was the source of the discrepancy. Moreover, our detailed results confirm the existence of a new partially deconfined phase which describes non-uniform black strings via the gauge/gravity duality. This phase exhibits universal features already predicted in quantum field theory.
We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is part
icularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).
