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What do these branching rules mean? \begin{eqnarray*} SO(6)_E &\to& SU(2)_\ell \times SU(2)_r \times U(1)_\Sigma \end{eqnarray*} I am taking these examples from a paper of Gukov (on p.51) but more …

This is the ABJM partition function on the 3-sphere, $$ Z(2) = \int \frac{d^2\mu}{(2\pi)^2} \frac{d^2\nu}{(2\pi)^2} \frac{\left[ 2 \sinh \frac{\mu_1 - \mu_2}{2}\right]^2\left[ 2 \sinh \frac{\nu_1 - …

Is there a link between the theory of Domino Tilings and the Ising Model? In the global qualitative sense that physicists use, the answer is "yes". The connections could go like this: The dimer m …

The answer to my question is "yes". Technically, it's a spin-TQFT but now I am trying to make sense of that answer. Dimers on surface graphs and spin structures. I David Cimasoni, Nicolai Resheti …

Without any regards to the physics or the geometry used to generate this result, let's examine the formula of Gukov (see p. 32): $$ \mathcal{I}_{SU(2)}(q,t) = \frac{1}{2}\sum_{m \in \mathbb{Z}}\int \ …

Reading this paper of Masahito Yamazaki and Kazuya Yonekura, I am having trouble turning the physics jargon into mathematical statements. He is talking about Yang-Mills theory over $\mathbb{R}^4$. P …

Something I really enjoy about Tao's writing is that he proves the same theorem over and over. While I complain a bit sometimes about clarity, this is a heuristic that I very much believe in. This …

I am trying to find a correspondence between 6-vertex model and an Aztec Diamond tiling. Here are the building blocks of the 8-vertex model: There seems to be more than one correspondence. I foun …

I am trying to understand what is a Higgs bundle as defined in this paper by Gukov and Pei. They say it is a pair $(E, \Phi)$ $E$ is a holomorphic principal $G^\mathbb{C}$ bundle $\Phi \in H^0(\S …

In a physics paper I found a very complicated Gaussian matrix model: $$ Z = \int \frac{d\mu}{(2\pi)^n} \frac{d\nu}{(2\pi)^n} \frac{ \prod_{i < j}\left[2 \sinh \frac{\mu_i - \mu_j}{2} \right]^2 \prod_ …

Recently there was a proof of the Wallis Product using quantum mechanics on the arXiv. However, there are many proofs of the result, Wikipedia has 4. Fine Print the first proof has on Wikipedia, the …

Let $M = \{ G(x) = 0 \} \subseteq \mathbb{P}^4$ be a quintic Calabi-Yau and $\mathbf{e} \in H^2(M, \mathbb{Z})$ such that $\int_M \mathbf{e}^3 = 5$. Then as $t \gg 1$: $$ \int_M e^{n \mathbf{e}} e …

I am reading Planar Diagrams by Brezin, Parisi, Itzykson and Zuber. If you specialize the discussion in section 5 there we seem to derive the eigenvalue distribution of $N \times N$ random Hermitian …

The definition of entanglement entropy in Quantum Field Theory involves decompositing a Hilbert space into a tensor product $\mathcal{H} = \mathcal{H}_A \otimes \mathcal{H}_B$. As an example, is it …

In physics papers, the massless free boson has a definition involving an action: $$ S(X) = \frac{1}{8\pi} \int d\sigma^2\, \partial X \overline{\partial X}$$ The random functions $X(z)$ are sample …