String Seminar

Large-N limit as a second quantization

In gauge/gravity duality, the information regarding the gravitational geometry (e.g., black hole and smooth exterior geometry) has to be encoded in gauge theory. Clearly, the color degrees of freedom (matrix degrees of freedom) should play the key role, because the duality can hold even when the gauge theory side is a matrix model. In this talk, I will suggest a simple way of encoding the geometry to matrices, along the line of Witten's work on the effective action of D-branes and strings, and the Matrix Theory conjecture by Banks, Fischler, Shenker and Susskind. Roughly speaking, eigenvalues of matrices can be identified with the location of the D-brane probe or extended objects such as black hole. 



Actually there is a famous argument against such simple interpretation advocated by Polchinski in 1998. His argument used generic properties of large-N gauge theory to show that the ground-state wave function delocalizes at large N, leading to a conflict with the locality in the bulk geometry. We show that this argument is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. In order to understand how the old argument fails, recently-discovered connection between color confinement and Bose-Einstein condensation is useful. This confinement-BEC connection has a striking consequence: in the SU(N) gauge theory, there is a partially-deconfined phase in which an SU(M)-subgroup is deconfined. Partial deconfinement, combined with the "eigenvalue = location" picture, provides us with a natural scenario to realize the idea in BFSS Matrix Theory conjecture --- extended objects, such as black hole, are realized as bound states of D-branes and strings, that look like non-commutative blocks in big matrices --- in the Maldacena-type gauge/gravity duality. In the large-N limit, various many-body states can be realized by considering block-diagonal matrix configurations, similarly to the BFSS proposal. Therefore, the large-N limit of gauge theory can be interpreted as the second quantization of the gravity side. 



If time permits, we will discuss how we might be able to check this proposal quantitatively, via classical or quantum simulations.  

Date:
Location:
zoom
Event Series:

An equilibrium approximation for quantum-informational observables in quantum many-body systems and gravity

Abstract: 

 

I will explain an approximation method that gives a simple universal expression for the Renyi entropies of an equilibrated pure state in a chaotic quantum many-body system. This expression is independent of the details of the initial state and hence reflects thermalization, while also being manifestly consistent with unitarity. I will discuss how applying this method to models of evaporating black holes leads to a derivation of replica wormholes, which have recently been used to address the information loss paradox in these models. More generally, this approach elucidates the role played by Euclidean path integrals in calculations of time-evolved Renyi entropies. It also helps address the question of whether an average over theories is needed in order to explain results from replica wormholes. I will also comment on work in progress on applications of this approximation method to other quantum-informational quantities.

Date:
Event Series:

Holographic correlators at finite temperature

Abstract: We consider weakly-coupled QFT in AdS at finite temperature. We compute the holographic thermal two-point function of scalar operators in the boundary theory. We present analytic expressions for leading corrections due to local quartic interactions in the bulk, with an arbitrary number of derivatives and for any number of spacetime dimensions. The solutions are fixed by judiciously picking an ansatz and imposing consistency conditions. The conditions include analyticity properties, consistency with the operator product expansion, and the Kubo-Martin-Schwinger condition. For the case without any derivatives we show agreement with an explicit diagrammatic computation. The structure of the answer is suggestive of a thermal Mellin amplitude. Additionally, we derive a simple dispersion relation for thermal two-point functions which reconstructs the function from its discontinuity.

 

Recording: https://uky.zoom.us/rec/play/Wf_ZpKnNEXDWMaQ4vk6XG0DKUI8mhjqC8p2O4ohSjt…

Date:
Event Series:

Quantum ergodicity and Euclidean Wormholes

 For a generic quantum-many-body system, quantum ergodicity is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this talk I will describe the correlation functions in the ergodic limit, making use of the causal symmetry breaking to construct an EFT describing the relevant universal late-time dynamics: the ramp and the plateau. I will also discuss the bulk interpretation of these results in terms of Euclidean wormholes.
 
 
Date:
Location:
zoom
Event Series:

Quantum computing for bosonic fields

Abstract: As universal quantum computers move from theoretical devices towards concrete

realizations, albeit still quite experimental, there is a lot of interest in
understanding whether outstanding problems in nuclear physics, like real-time
dynamics and bulk properties of nuclear matter, could be solved using these 
machines. For these applications we need to represent in hardware quantum field 
theories for both fermionic and bosonics degrees of freedom. Discretized fermionic 
fields can be represented fully since they map naturally onto qbits. On the other 
hand bosonic degrees of freedom--which even for discretized fields require an 
infinite dimensional Hilbert space at each site--require a truncation. In this 
talk I discuss two directions we investigated to address this problem: using 
discrete subsets to represent gauge degrees of freedom, or truncations in a dual 
space that that preserve the original symmetries of the theory. As test-cases 
for these ideas we use pure-gauge QCD and the sigma-model.
Date:
Event Series:

On QFT in de Sitter

I will discuss the tools we are developing to calculate correlation functions of primordial inflationary perturbations. In this talk we will focus on the limit where gravitational excitations are neglected and the cosmological spacetime is assumed to be exactly de Sitter. Even in this simplifying limit, which corresponds to a Quantum Field Theory on a de Sitter background, very few examples of explicit analytic calculations exist and little is known about basic properties of the correlators. I will show that for any dS QFT there exists a theory formulated in a Euclidean Anti-de SItter space and which reproduces all the correlation functions. This leads to major technical simplifications and allows to demonstrate various analytic properties of the cosmological observables. Understanding of these properties has both phenomenological applications in inflation, as well as provides some hints about more fundamental description for cosmological spacetimes.

 

Recording: https://uky.zoom.us/rec/share/qKxeMiQf7ptDU4YiMncdBclJ4DwICuWH8TiAcj36R…

Date:
Event Series:

Derivation of AdS/CFT for Vector Models

We derive an explicit map between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two and to all orders in 1/N, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields.

Date:
Location:
zoom
Event Series:

A hierarchy of complexity growth from integrability and chaos

Quantum complexity has been conjectured to be relevant for black hole interiors.  In particular, Susskind has conjectured a generic form of complexity growth and saturation for maximally chaotic systems like black holes.  Using geodesic complexity techniques, we study the complexity of time evolution in free, integrable, and chaotic systems with N degrees of freedom.  We demonstrate that the growth rate of this complexity is related to more familiar properties of physical theories like 1) the existence of creation/annihilation operators and 2) smeared thermal two-point functions.  Using these properties, we find that the complexity saturates in free, integrable, and chaotic theories at time scales which are on the order of N^{1/2}, polynomial in N, and exponential in N, respectively.  Our results in the free theory improve an existing bound in the complexity theory literature, and our results in chaotic theories are based only on coarse properties of the spectrum and eigenstates.

 

Recording: https://uky.zoom.us/rec/share/RVdvrcvcN5ExKFWdowQzvzkuLZNQ7w1Q97TpxAfMp1DJDgmNTf_hAgS30IRSD5-S.h_63aSEfE-Bt4_F9

Date:
Event Series:

Crossing symmetric dispersion relations in QFTs and CFTs

I will discuss crossing symmetric dispersion relations in QFTs and CFTs. I will talk about connections with Polyakov’s 1974 work, the crossing symmetric Polyakov-Mellin bootstrap, and connections with fixed-t dispersion relations. I will also talk about generalized Froissart bounds in QFTs which follow from this approach.

***Please note unusual time

 

Date:
Location:
zoom
Event Series:

Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians

Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
 
We introduce a framework for constructing a quantum error correcting code from any classical error correcting code. This includes CSS codes and goes beyond the stabilizer formalism to allow quantum codes to be constructed from classical codes that are not necessarily linear or self-orthogonal. We give an algorithm that explicitly constructs quantum codes with linear distance and constant rate from classical codes with a linear distance and rate. As illustrations for small size codes, we obtain Steane's 7−qubit code uniquely from Hamming's [7,4,3] code, and obtain other error detecting quantum codes from other explicit classical codes of length 4 and 6. Motivated by quantum LDPC codes and the use of physics to protect quantum information, we introduce a new 2-local frustration free quantum spin chain Hamiltonian whose ground space we analytically characterize completely. By mapping classical codewords to basis states of the ground space, we utilize our framework to demonstrate that the ground space contains explicit quantum codes with linear distance. This side-steps the Bravyi-Terhal no-go theorem because our work allows for more general quantum codes beyond the stabilizer and/or linear codes. We hesitate to call this an example of {\it subspace} quantum LDPC code with linear distance.
 

Recording: https://uky.zoom.us/rec/share/XomugVk3-_mSqWNWTwioA1Uht2ckNNxAunRvIKmYMLRyQ5SRXJCaztf6IyaSOCgP.XVtcRvqyBGtz-clq

Date:
Location:
zoom
Event Series: