The research-level tag applies to questions that arise in graduate and post-secondary work. These questions often require domain-specific knowledge and could not be answered from a general source or may be beyond the level typically covered by Wikipedia and other popular sources. research-level ...

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3k views

What is a resonating valence bond (RVB) state?

There's something known as a "resonating valence bond" (RVB) state, which plays a role in at least some attempts to understand physics of high-$T_c$ superconductors. This, roughly, involves a state ...
14
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1answer
132 views

Instanton Moduli Space with a Surface Operator

I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator. Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are ...
14
votes
1answer
213 views

Do Gauge Theories (CFTs) Have Phase Transitions as the 't Hooft Coupling is Varied?

With an eye toward AdS/CFT, I'm wondering if large $N$ CFTs have a (quantum) phase transition as the 't Hooft coupling is varied. To be more specific -- if I look at correlation functions of ...
14
votes
1answer
199 views

Monte Carlo integration over space of quantum states

I am currently facing the problem of calculating integrals that take the general form $\int_{R} P(\sigma)d\sigma$ where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
14
votes
1answer
925 views

Boundary conditions / uniqueness of the propagators / Green's functions

My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields. It is well known that the Green's function for the Laplace ...
14
votes
1answer
445 views

Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold

In Witten's paper Quantum Field Theory and the Jones Polynomial, he mentioned that: Geometers have long known that (via de Rham theory) the self-dual and anti-self-dual Maxwell equations are ...
14
votes
1answer
229 views

6d Massive Gravity

Massive gravity (with a Fierz-Pauli mass) in 4 dimensions is very well-studied, involving exotic phenomena like the vDVZ discontinuity and the Vainshtein effect that all have an elegant and physically ...
14
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1answer
191 views

Phase Transition in the Ising Model with Non-Uniform Magnetic Field

Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by $$ ...
14
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2answers
395 views

Newtonian gravity from the holographic principle?

Can one understand Newton's law of gravitation using the holographic principle (or does such reasoning just amount to dimensional analysis)? Following an argument similar to one given by Erik ...
14
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0answers
107 views

Minimal strings and topological strings

In http://arxiv.org/abs/hep-th/0206255 Dijkgraaf and Vafa showed that the closed string partition function of the topological B-model on a Calabi-Yau of the form $uv-H(x,y)=0$ coincides with the free ...
13
votes
5answers
429 views

Other processes than formal power series expansions in quantum field theory calculations

I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e. , what dynamical systems ...
13
votes
1answer
457 views

Covariant derivatives

I need correctly define covariant derivatives on the coset space $G/H$, where a group $G \equiv \{X_i, Y_a\}$ ($X$ and $Y$ are generators) have a subrgroup $H \equiv \{X_i\}$ Lie algebra of $G$ has ...
13
votes
3answers
245 views

Status of local gauge invariance in axiomatic quantum field theory

In his recent review... Sergio Doplicher, The principle of locality: Effectiveness, fate, and challenges, J. Math. Phys. 51, 015218 (2010), doi ...Sergio Doplicher mentions an important open ...
13
votes
1answer
283 views

realization of: CFT generating fuction = AdS partition function

An important aspect of the AdS/CFT correspondence is the recipe to compute correlation functions of a boundary operator $\mathcal{O} $ in terms of the supergravity fields in the interior of the ...
13
votes
2answers
1k views

Literature on fractal properties of quasicrystals

At the seminar where the talk was about quasicrystals, I mentioned that some results on their properties remind the fractals. The person who gave the talk was not too fluent in a rigor mathematics ...
13
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2answers
678 views

Topological twists of SUSY gauge theory

Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this theory has 3 ...
13
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2answers
364 views

A resource theory of quantum discord?

Local Operations and Classical Communication (LOCC) is the classic paradigm for studying entanglement. These are things that are `cheap' and unable to produce entanglement as a resource for a quantum ...
13
votes
3answers
4k views

Quantum memories: What are they?

Searching the literature for the term "quantum memory" seems to bring up results from two different communities. On the one hand there are quantum opticians, who see a quantum memory as something ...
13
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1answer
96 views

Physical interpretation of superstrings

The scalar fields $X^\mu$ in bosonic string theory have a clear physical interpretation - they describe the embedding of the string in spacetime. Adding fermionic fields on the worldsheet is a ...
13
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1answer
213 views

What is the Holevo-Schumacher-Westmoreland capacity of a Pauli channel?

Suppose you are given an $n$-qubit quantum channel defined as $\mathcal{E}(\rho) = \sum_{i} p_i X_i \rho X_i^\dagger$, where $X_i$ denotes an $n$-fold tensor product of Pauli matrices and $\{p_i\}$ is ...
13
votes
2answers
405 views

Normalization of the Chern-Simons level in $SO(N)$ gauge theory

In a 3d SU(N) gauge theory with action $\frac{k}{4\pi} \int \mathrm{Tr} (A \wedge dA + \frac{2}{3} A \wedge A \wedge A)$, where the generators are normalized to $\mathrm{Tr}(T^a ...
13
votes
1answer
653 views

Lagrangian for Euler Equations in general relativity

The stress energy tensor for relativistic dust $$ T_{\mu\nu} = \rho v_\mu v_\nu $$ follows from the action $$ S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x = -\int c \sqrt{p_\mu ...
13
votes
2answers
247 views

Decoherence and measurement in NMR

It seems that the Bloch equations, or a suitable generalization thereof, are enough to phenomenologically model the measurement process in NMR. Has anyone attempted a fully quantum mechanical model ...
13
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2answers
651 views

How can we define BF theory on a general 4-manifold?

(I have rewritten the question some, with new understanding) 4d BF theory is classically presented as the TFT arising from the Lagrangian $B\wedge F$, where $B$ is an abelian 2-connection (locally ...
13
votes
1answer
836 views

Is there a “covariant derivative” for conformal transformation?

A primary field is defined by its behavior under a conformal transformation $x\rightarrow x'(x)$: $$\phi(x)\rightarrow\phi'(x')=\left|\frac{\partial x'}{\partial x}\right|^{-h}\phi(x)$$ It's fairly ...
13
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2answers
401 views

Holographic Renormalization in non-AdS/non-CFT

In AdS/CFT, the story of renormalization has an elegant gravity dual. Regularizing the theory is done by putting a cutoff near the conformal boundary of AdS space, and renormalization is done by ...
13
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2answers
138 views

Uniqueness of supersymmetric heterotic string theory

Usually we say there are two types of heterotic strings, namely $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$. (Let's forget about non-supersymmetric heterotic strings for now.) The standard argument ...
13
votes
1answer
85 views

Local Fermionic Symmetry

That is perhaps a bit of an advertisement, but a couple of collaborators and myself just sent out a paper, and one of the results there is a little bit surprising. We found (in section 6E) a fermionic ...
13
votes
1answer
605 views

What are the limitations of the superspace formalism?

Just from reading this slightly technical introduction to supersymmetry and watching these Lenny Susskind lectures, I thought that the Lagrangian of any "reasonable" supersymmetric theory can always ...
13
votes
2answers
520 views

What does the sum of two qubits tell about their correlations?

How much can I learn about correlations between two quits by measuring the sum of their values? What is the best way to formalize such a question? Below is my original, longer formulation of ...
13
votes
2answers
431 views

How do you simulate chiral gauge theories on a computer?

David Tong and Lubos Motl have argued that our universe can't possibly be a digital computer simulation because chiral gauge theories can't be discretized, and the Standard Model is a chiral gauge ...
13
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1answer
53 views

SuperHiggs Mechanism on different Backgrounds & Compactifications

I've been studying Bagger & Giannakis paper on the SuperHiggs Mechanism found here. The paper shows how SUSY is broken by a $B_{\mu\nu}$ gauge field background restricted to $T^3$ in $M^7\times ...
13
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0answers
180 views

Super Lie-infinity algebra of closed superstring field theory?

Bosonic closed string field theory is famously governed by a Lie n-algebra for $n = \infty$ whose $k$-ary bracket is given by the genus-0 (k+1)-point function in the BRST complex of the string. One ...
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0answers
419 views

Hypersingular Boundary Operator in Physics

This has been a question I've been asking myself for quite some time now. Is there a physical Interpretation of the Hypersingular Boundary Operator? First, let me give some motivation why I think ...
12
votes
4answers
1k views

Rigorous proof of Bohr-Sommerfeld quantization

Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In ...
12
votes
1answer
542 views

What is a “free” non-Abelian Yang-Mill's theory?

I hope this question will not be closed down as something completely trivial! I did not think about this question till in recent past I came across papers which seemed to write down pretty much ...
12
votes
2answers
289 views

Random Walk Randomly Reflected

Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory. In this case, I will ...
12
votes
1answer
205 views

Are possible gauge fields in a Lagrangian theory always determined by the structure of the charged degrees of freedom?

An elementary example to explain what I mean. Consider introducing a classical point particle with a Lagrangian $L(\mathbf{q} ,\dot{\mathbf{q}}, t)$. The most general gauge transformation is $L ...
12
votes
1answer
101 views

Relationship between Weak Cosmic Censorship and Topological Censorship

The weak cosmic censorship states that any singularity cannot be in the causual past of null infinity (reference). The topological censorship hypothesis states that in a globally hyperbolic, ...
12
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2answers
95 views

Numerical Analysis of Elliptic PDEs

I am looking for an elementary reference regarding issues of stability in numerical analysis of non-linear elliptic PDEs, particularly using the finite difference method (but something more ...
12
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2answers
182 views

How much of the Capelli-Itzykson-Zuber ADE-classification of su(2)-conformal field theories can one see perturbatively?

In their celebrated work, Capelli Itzykson and Zuber established an ADE-classification of modular invariant CFTs with chiral algebra $\mathfrak{su}(2)_k$. How much of that classification can one ...
12
votes
2answers
882 views

Do topological superconductors exhibit symmetry-enriched topological order?

Gapped Hamiltonians with a ground-state having long-range entanglement (LRE), are said to have topological order (TO), while if the ground state is short-range entangled (SRE) they are in the trivial ...
12
votes
4answers
793 views

What exactly does the holographic principle say?

Does the holographic principle say given a spatially enclosing boundary satisfying the Bousso condition on expansion parameters, the log of the number of microstates in its interior is bounded by ...
12
votes
1answer
196 views

CHSH violation and entanglement of quantum states

How is the violation of the usual CHSH inequality by a quantum state related to the entanglement of that quantum state? Say we know that exist Hermitian and unitary operators $A_{0}$, $A_{1}$, ...
12
votes
2answers
1k views

Vasiliev gravity and “holographic” entanglement

It has been proposed that AdS/CFT arises because of the entanglement structure of quantum field theories, e.g. see the discussion which occurred right here. Until now I have been skeptical of the ...
12
votes
1answer
686 views

What is the CFT dual to pure gravity on AdS$_3$?

Pure $2+1$-dimensional gravity in $AdS_3$ (parametrized as $S= \int d^3 x \frac{1}{16 \pi G} \sqrt{-g} (R+\frac{2}{l^2})$) is a topological field theory closely related to Chern-Simons theory, and at ...
12
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1answer
348 views

Supersymmetric Noether theorem and supercurrents — invariance requirements

Consider $\mathcal{N}=1,d=4$ SUSY with $n$ chiral superfields $\Phi^i,$ Kaehler potential $K,$ superpotential $W$ and action ($\overline{\Phi}_i$ is complex conjugate of $\Phi^i$) $$ S= \int d^4x ...
12
votes
1answer
696 views

Asymptotic symmetry algebra

So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for ...
12
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1answer
748 views

Entanglement in time

Quantum entanglement links particles through time, according to this study that received some publicity last year: New Type Of Entanglement Allows 'Teleportation in Time,' Say Physicists at The ...
12
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0answers
218 views

Compactifying on a circle and the exchange of R and NS sectors

I've noticed a general phenomenon in compactifying on a circle where if you start with, say, an NS field, then the KK fields with an index along the circle will be in the R sector, and those without ...