Instantons, symmetries and anomalies in five dimensions

Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d$$ \mathcal{N} $$ N = 1 theories, we initiate a systematic study of compactifications of 5d$$ \mathcal{N} $$ N = 1 SCFTs on Riemann surfaces to 3d$$ \mathcal{N} $$ N = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $$ {E}_{N_f+1} $$ E N f + 1 SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.

Section: Jhep09(2021)149mentioning

confidence: 99%

“…Nevertheless, there are some known results on these subjects. See for instance[43] for discrete 0-form symmetries of 5d SCFTs,[44][45][46] for higher form symmetries of 5d SCFTs, and[47] for anomalies involving these symmetries.…”

mentioning

confidence: 99%

Compactifying 5d superconformal field theories to 3d

Sacchi

Sela

Zafrir

2021

“…Recently, there has been much interest in understanding the spectrum of extended operators such as Wilson lines and surface defects in field theories [1][2][3][4][5][6]. In fact, there are theories with the same local structure that differ only by their spectrum of extended operators [7] and consequently by their partition functions, further highlighting the importance of their presence.…”

Section: Introductionmentioning

confidence: 99%

Maruyoshi-Song flows and defect groups of $$ {\mathrm{D}}_{\mathrm{p}}^{\mathrm{b}} $$(G) theories

Hosseini

Moscrop

2021

We study the defect groups of $$ {D}_p^b $$ D p b (G) theories using geometric engineering and BPS quivers. In the simple case when b = h∨(G), we use the BPS quivers of the theory to see that the defect group is compatible with a known Maruyoshi-Song flow. To extend to the case where b ≠ h∨(G), we use a similar Maruyoshi-Song flow to conjecture that the defect groups of $$ {D}_p^b $$ D p b (G) theories are given by those of G(b)[k] theories. In the cases of G = An, E6, E8 we cross check our result by calculating the BPS quivers of the G(b)[k] theories and looking at the cokernel of their intersection matrix.

“…In particular, suppose that in addition to monopoles, we now add fundamental strings charged under B 2 . 9 The equation of motion for B 2 then gives…”

Section: Jhep11(2021)053mentioning

confidence: 99%

“…These symmetries have been occasionally discussed in the literature, especially in 5d gauge theories where tr(F ∧ F ) generates an ordinary 0-form global symmetry under which instantons are charged particles [7][8][9], and in 6d gauge theories where such a current generates a 1-form symmetry under which strings are charged [10][11][12]. 1 However, to the best of our knowledge there has been little systematic study of general Chern-Weil global symmetries.…”

Section: Jhep11(2021)053 1 Introductionmentioning

confidence: 99%

Chern-Weil global symmetries and how quantum gravity avoids them

Heidenreich

McNamara

Montero

et al. 2021

We draw attention to a class of generalized global symmetries, which we call “Chern-Weil global symmetries,” that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths, such as F2 ∧ H3 and tr($$ {F}_2^2 $$ F 2 2 ), and their conservation follows from Bianchi identities. As a result, they are not easy to break. However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity.