Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1309.0697

On the 6d origin of discrete additional data of 4d gauge theories

Yuji Tachikawa
View original source ↗Read source document ↗Export metadata ↓

Abstract

Starting with a choice of gauge algebras, specification of a 4d gauge theory involves additional data, namely the gauge groups and the discrete theta angles. Equivalently, one needs to specify the set of charges of allowed line operators. In this note, we study how these additional data are represented in 6d, when the 4d theory in question is an N=4 super Yang-Mills theory or an N=2 class S theory. We will see that the Z_N symmetry of the so-called T_N theory plays an important role. As a byproduct, we will find that the superconformal index of class S theories can be refined so that it can give 2d q-deformed Yang-Mills theory with different gauge groups associated to the same gauge algebra.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yuji Tachikawa. 2014-02-10. On the 6d origin of discrete additional data of 4d gauge theories. https://doi.org/10.1007/jhep05(2014)020

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Giant graviton integrated correlators at finite coupling and all orders in $1/N$

We study the giant graviton integrated correlator in SU$(N)$ $\mathcal{N}=4$ super Yang-Mills at finite complexified coupling $τ$. Despite the formidable complexity arising from the heavy nature of the operators considered, the large-$N$ expansion simplifies dramatically and exhibits manifest modular invariance. At each order in $1/N$, the expansion coefficients are linear combinations of non-holomorphic Eisenstein series thus capturing the full spectrum of perturbative and non-perturbative effects in the Yang-Mills coupling. Furthermore, we find additional contributions which are modular functions exponentially suppressed in $N$. In the 't Hooft limit, this yields an all-orders result in the $1/N$ expansion at arbitrary coupling $λ$, extending beyond prior results of leading orders. For the U$(N)$ theory, we obtain a closed-form expression valid for all $N$ and $τ$, and show that the coupling-dependent sector of the large-$N$ expansion is universal between SU$(N)$ and U$(N)$ to all orders. Crucially, we exploit the integrated correlator constraints and determine the giant graviton correlator itself to two-loop order at finite $N$, previously only accessible in the planar limit.

hep-th↗
arXiv2026

Bulk Monodromy of Logarithmic Graviton Descendants in Critical Topologically Massive Gravity

We study the bulk analytic structure of the logarithmic graviton and its global descendants in critical topologically massive gravity. Starting from the Grumiller--Johansson mode, we complexify the radial coordinate and derive its monodromy directly from the branch structure and winding data of the logarithmic radial factor. We then construct the global logarithmic descendants by explicit differential action and show that each descendant decomposes into a universal logarithmic contribution and a log-free meromorphic remainder. This implies a universal unipotent monodromy throughout the global descendant space. The associated nilpotent operator, obtained directly from the bulk analytic continuation, is shown to intertwine the full global $SL(2,\mathbb R)_L\times SL(2,\mathbb R)_R$ action. These results provide a direct bulk analytic realization of the logarithmic structure, linking radial monodromy and global conformal symmetry.

hep-th↗
arXiv2026

How traversable is a traversable wormhole?

To answer the above question, we study low-frequency scattering in the four-dimensional traversable wormhole of Maldacena, Milekhin, and Popov. The resulting transmission probabilities reveal that wormhole traversability depends strongly on the nature of the probe. For scalar probes, both neutral and charged, traversability depends on the time scale. On time scales of order the light-crossing time after sending in a signal, the transmission is parametrically suppressed, with most of the incoming signal reflected or temporarily trapped inside the wormhole throat. As time progresses, the trapped signal gradually leaks out, so that at late times the accumulated transmission cross-section approaches one half of the corresponding black hole absorption cross-section. Despite this generic suppression at low frequencies, the transmission spectrum also exhibits resonant frequencies at which transmission becomes perfect. Charged massless fermions tell a very different story. Unlike scalars, they traverse the wormhole with essentially unit probability at low energies. The same mechanism underlies their efficient absorption by magnetic black holes and realizes a channel closely analogous to the Callan-Rubakov effect, revealing unexpected connections with monopole-fermion scattering. Putting everything together, we conclude that scalar probes are best suited for uncovering distinct features of these magnetic wormholes, while charged massless fermions are the ideal carriers of information through them.

hep-th↗