Related papers: Renormalization and blow up for the critical Yang-…

In order to deepen our understanding of the nature of the deconfinement phase transition for various gauge groups, we investigate SU(4) Yang-Mills theory in 2+1 dimensions. We find that the transition is weakly first order. We perform…

We present a renormalizability proof for spontaneously broken SU(2) gauge theory based on Flow Equations. It is a conceptually and technically simplified version of the earlier paper [KM] including some extensions. The proof of [KM] also…

We consider the semilinear wave equation $$\partial_t^2 u -\Delta u =f(u), \quad (x,t)\in \mathbb{R}^N\times [0,T),\qquad (1)$$ with $f(u)=|u|^{p-1}u\log^a (2+u^2)$, where $p>1$ and $a\in \mathbb{R}$. We show an upper bound for any blow-up…

We prove that the critical Wave Maps equation with target $S^2$ and origin $\mathbb{R}^{2+1}$ admits energy class blow up solutions of the form $$u(t,r)=Q(\lambda(t)r)+\epsilon(t,r)$$where $Q: \mathbb{R}^2 \to S^2$ is the ground state…

We study the heat flow for Yang-Mills connections on $\mathbb R^d \times SO(d)$. It is well-known that in dimensions $5 \leq d \leq 9$ this model admits homothetically shrinking solitons, i.e., self-similar blowup solutions, with an…

We consider particle-like and black holes solutions of the Einstein-Yang-Mills system with positive cosmological constant in d>4 spacetime dimensions. These configurations are spherically symmetric and present a cosmological horizon for a…

We compute the static potential associated to the locally 1/2 BPS Wilson loop in ${\cal N}$=4 supersymmetric Yang-Mills theory with ${\cal O}(\lambda^2/r)$ accuracy. We also resum the leading logarithms, of ${\cal…

In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…

We analyze the finite-time blow-up of solutions of the heat flow for $k$-corotational maps $\mathbb R^d\to S^d$. For each dimension $d>2+k(2+2\sqrt{2})$ we construct a countable family of blow-up solutions via a method of matched…

The (2k+2)-dimensional Einstein-Yang-Mills equations for gauge group SO(2k) (or SU(2) for k=2 and SU(3) for k=3) are shown to admit a family of spherically-symmetric magnetic monopole solutions, for both zero and non-zero cosmological…

The renormalization of $\mathcal{N}=1$ Super Yang-Mills theory with the presence of the local composite operators $AA$, $A_\mu \gamma_\mu \lambda$ and $\bar{\lambda}\lambda$ is analyzed in the Wess-Zumino gauge, employing the Landau…

In this paper we construct an exact spherically symmetric black hole solution with a power Yang-Mills (YM) source in the context of $4D$ Einstein Gauss-Bonnet gravity ($4D$ EGB). We choose our source as $(F_{\mu\nu}^{(a)}F^{\mu\nu(a)})^q$,…

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, a Schr\"odinger-type equation with a nonlocal, convolution-type nonlinearity: $iu_t+\Delta u +\left(|x|^{-(d-2)} \ast |u|^{p} \right) |u|^{p-2}u = 0,…

We establish renormalizability of the full spectral action for the Yang-Mills system on a flat 4-dimensional background manifold. Interpreting the spectral action as a higher-derivative gauge theory, we find that it behaves unexpectedly…

Based on our companion paper [Krieger-Schmid, 2024], we show that the 4D energy critical Zakharov system admits finite time type II blow up solutions. The main new difficulty this work deals with is the appearance of a term in the…

The $\gamma_i$-deformed $\mathcal{N}=4$ super-Yang-Mills theory is a non-supersymmetric deformation of the maximally-supersymmetric gauge theory in four dimensions which is conformally-invariant at the planar level. At the non-planar level…

We consider asymptotically self-similar blow-up profiles of the thin film equation consisting of a stabilising fourth order and destabilising second order term. It has previously been shown that blow up is only possible when the exponent in…

We study five dimensional non critical type 0 string theory and its correspondence to non supersymmetric Yang Mills theory in four dimensions. We solve the equations of motion of the low energy effective action and identify a class of…

We consider the following nonlinear Schr\"{o}dinger equation with an inverse potential: \[ i\frac{\partial u}{\partial t}+\Delta u+|u|^{\frac{4}{N}}u\pm\frac{1}{|x|^{2\sigma}}u=0 \] in $\mathbb{R}^N$. From the classical argument, the…

For the quintic, mass critical generalized Korteweg-de Vries equation, for any $\nu \in (\frac{1}{2}, 1)$, we prove the existence of solutions in the energy space that blow up in finite time $T>0$ with the blow-up rate $\|\partial_x…