arxiv: 2605.12594 · v1 · submitted 2026-05-12 · ✦ hep-th

Recognition: unknown

String probes, simple currents, and the no global symmetries conjecture

Guglielmo Lockhart , Luca Novelli , Yann Proto

Authors on Pith no claims yet

Pith reviewed 2026-05-14 20:28 UTC · model grok-4.3

classification ✦ hep-th

keywords center one-form symmetriessimple currentsstring probesheterotic compactificationsgauge group topologyquantum gravityBPS particlesworldsheet currents

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The pith

Chiral simple currents extending the worldsheet algebra of faithful string probes reproduce obstructions to gauging center one-form symmetries in six and eight dimensions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines center one-form symmetries through the lens of faithful string probes, which are extended objects where the gauge symmetry is realized as a holomorphic current algebra. It argues that gauged versions of these symmetries correspond to chiral simple currents that extend the current algebra on the worldsheet. The consistency conditions required for these extensions match and generalize known field-theoretic and geometric obstructions in six and eight dimensions. This is checked in heterotic string compactifications and used to find the gauge group topology for a class of six-dimensional models. The results also clarify why certain BPS particles are needed for consistency in six-dimensional supergravity after circle reduction.

Core claim

The worldsheet counterpart of gauged center one-form symmetries is the existence of chiral simple currents extending the current algebra for faithful string probes that realize the gauge symmetry as a holomorphic current algebra. The consistency condition for such extensions reproduce and generalize known field theoretic and geometric obstructions to the gauging of center one-form symmetries in six and eight dimensions.

What carries the argument

Faithful string probes realizing the gauge symmetry as a holomorphic current algebra, extended by chiral simple currents.

If this is right

The gauge group topology of recently identified six-dimensional models with no known F-theoretic realization can be inferred from the presence of such currents.
In six-dimensional supergravity, gauged center one-form symmetries require specific BPS particles for consistency upon circle reduction.
The consistency conditions generalize known obstructions to gauging in both six and eight dimensions.
Composite higher-spin chiral currents appear in several models, suggesting a stringy generalization of center one-form symmetries.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This worldsheet approach could be applied to test similar symmetry constraints in compactifications beyond the heterotic string.
The higher-spin currents may point to new bulk structures in the effective theory that go beyond standard one-form symmetry descriptions.
Analogous probes using other extended objects could help classify global symmetry possibilities across quantum gravity models.

Load-bearing premise

The worldsheet counterpart of gauged center one-form symmetries is precisely the existence of chiral simple currents extending the current algebra for faithful string probes.

What would settle it

A consistent string compactification with a gauged center one-form symmetry but no corresponding chiral simple current extension for its faithful string probes would falsify the proposed correspondence.

read the original abstract

Center one-form symmetries in consistent quantum gravity theories are expected to be either broken or gauged, thereby determining the global form of the gauge group. We shed light on this expectation from the perspective of distinguished extended objects, which we denote by faithful string probes, for which the gauge symmetry is realized as a holomorphic current algebra. We argue that the worldsheet counterpart of gauged center one-form symmetries is the existence of chiral simple currents extending the current algebra. Accordingly, we show that the consistency condition for such extensions reproduce and generalize known field theoretic and geometric obstructions to the gauging of center one-form symmetries in six and eight dimensions. We verify this picture in a number of examples arising from heterotic string compactifications, and apply it to infer the gauge group topology of a recently identified class of six-dimensional models with no known F-theoretic realization. In 6d supergavity, our results also clarify an observation of Kim and Vafa on the existence of BPS particles required for consistency upon circle reduction: these particles arise from worldsheet simple currents whose existence is dictated by the presence of a gauged center one-form symmetry. Intriguingly, in several models across different dimensions we find composite higher-spin chiral currents beyond the current algebra, hinting at a stringy generalization of center one-form symmetries in the bulk.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper identifies chiral simple currents as the worldsheet signature of gauged center one-form symmetries for faithful string probes, which reproduces known obstructions but assumes the mapping rather than deriving it generally.

read the letter

The core move is to treat the existence of chiral simple current extensions of the holomorphic current algebra as the worldsheet counterpart to gauging center one-form symmetries in the bulk. This lets them recover the standard field-theoretic and geometric obstructions in six and eight dimensions, check it against heterotic examples, and then use it to constrain gauge group topology in some six-dimensional models that lack known F-theory realizations. They also connect it to the BPS particles Kim and Vafa noted are needed for consistency after circle reduction. That part is useful and concrete for people building six-dimensional models. The heterotic checks give it some grounding. The main limitation is that the central equivalence is motivated by the probe construction and specific examples rather than shown to be necessary and sufficient in general. Without a derivation that this is exactly the worldsheet signature of bulk gauging, the reproduction of obstructions stays tied to the chosen probes and could miss other possibilities. The abstract states the consistency conditions reproduce prior results, but the full argument for why simple currents are the precise counterpart is not laid out here. This is worth a serious referee for the applications to new models and the clarification on the circle reduction, even though the mapping needs more work to stand on its own. Readers working on global symmetries in string compactifications would get the most from it.

Referee Report

1 major / 1 minor

Summary. The paper claims that the worldsheet counterpart of gauged center one-form symmetries is the existence of chiral simple currents extending the holomorphic current algebra for faithful string probes realizing gauge symmetry as a current algebra. It argues that consistency conditions on such extensions reproduce and generalize known field-theoretic and geometric obstructions to gauging center one-form symmetries in six and eight dimensions. This is verified in heterotic string compactification examples, applied to infer gauge group topology in a class of six-dimensional models without known F-theory realizations, and used to clarify the Kim-Vafa observation on required BPS particles upon circle reduction in 6d supergravity. The work also notes composite higher-spin chiral currents in several models, suggesting a possible stringy generalization of center symmetries.

Significance. If the proposed worldsheet-bulk correspondence holds, the manuscript offers a useful string-theoretic lens on the no global symmetries conjecture by connecting worldsheet current algebra extensions to bulk gauge group topology constraints. It reproduces established obstructions in 6d and 8d while extending the approach to new models, and the explicit checks in heterotic examples provide concrete grounding. The clarification of BPS particle requirements adds a link to effective field theory consistency. The observation of higher-spin currents hints at broader implications, though the overall significance depends on strengthening the foundational mapping.

major comments (1)

Abstract: The central claim that consistency conditions on chiral simple current extensions reproduce field-theoretic obstructions assumes that such extensions are precisely the worldsheet signature of gauged center one-form symmetries. This identification is motivated by heterotic examples but lacks a general derivation establishing necessity and sufficiency (as opposed to a sufficient condition in specific cases), which is load-bearing for the reproduction of obstructions and the generalization beyond the probe construction.

minor comments (1)

The terms 'faithful string probes' and the precise notion of current algebra extension would benefit from an earlier, more formal definition or reference to standard CFT literature on simple currents to improve accessibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed reading and the constructive comment on the foundational identification in the abstract. We address the point below and will make targeted revisions to clarify the scope of the argument without overstating the generality of the derivation.

read point-by-point responses

Referee: Abstract: The central claim that consistency conditions on chiral simple current extensions reproduce field-theoretic obstructions assumes that such extensions are precisely the worldsheet signature of gauged center one-form symmetries. This identification is motivated by heterotic examples but lacks a general derivation establishing necessity and sufficiency (as opposed to a sufficient condition in specific cases), which is load-bearing for the reproduction of obstructions and the generalization beyond the probe construction.

Authors: We agree that the identification is presented as an argument motivated by the faithful probe construction and verified explicitly in heterotic examples, rather than derived from first principles as a necessary and sufficient condition in full generality. The manuscript frames the statement with 'we argue that' and 'the worldsheet counterpart,' and the obstructions are reproduced within this framework. To address the concern, we will revise the abstract and the opening of Section 2 to state explicitly that the correspondence is established as a sufficient condition for the probe sector and that consistency of the simple-current extensions reproduces the known obstructions in all checked cases; we will also add a brief discussion of why the heterotic realizations provide supporting evidence for the broader applicability while acknowledging the absence of a model-independent necessity proof at this stage. revision: partial

Circularity Check

0 steps flagged

No significant circularity; consistency conditions match external obstructions via argued but non-reductive correspondence

full rationale

The paper posits an identification between gauged center one-form symmetries and the existence of chiral simple current extensions for faithful string probes, then shows that consistency conditions on such extensions reproduce and generalize known field-theoretic and geometric obstructions in 6d and 8d. This reproduction is checked against external benchmarks (prior obstructions) and verified in heterotic examples before application to new models. No step reduces a claimed prediction or derivation to an input by construction, self-definition, or self-citation chain; the central claim retains independent content from the CFT consistency analysis and external matching, qualifying as self-contained against benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

Relies on standard quantum gravity assumptions about center one-form symmetries and introduces new concepts like faithful string probes and their current algebra realization without external independent evidence.

axioms (2)

domain assumption Center one-form symmetries in consistent quantum gravity theories are expected to be either broken or gauged.
Opening expectation stated in the abstract that frames the entire analysis.
domain assumption Gauge symmetry is realized as a holomorphic current algebra for faithful string probes.
Core premise enabling the worldsheet perspective on bulk symmetries.

invented entities (2)

faithful string probes no independent evidence
purpose: Distinguished extended objects realizing gauge symmetry as holomorphic current algebra to probe center one-form symmetries.
Newly introduced objects central to the argument; no independent evidence outside the framework provided.
chiral simple currents no independent evidence
purpose: Worldsheet counterpart of gauged center one-form symmetries that extend the current algebra.
Key new connection argued to reproduce bulk obstructions; no independent falsifiable handle given.

pith-pipeline@v0.9.0 · 5533 in / 1441 out tokens · 31588 ms · 2026-05-14T20:28:11.932515+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

136 extracted references · 136 canonical work pages · 50 internal anchors

[1]

McNamara and C

J. McNamara and C. Vafa,Cobordism Classes and the Swampland,1909.10355

work page arXiv 1909
[2]

Monopoles, Duality, and String Theory

J. Polchinski,Monopoles, duality, and string theory,Int. J. Mod. Phys. A19S1 (2004) 145–156, [hep-th/0304042]

work page internal anchor Pith review Pith/arXiv arXiv 2004
[3]

Symmetries and Strings in Field Theory and Gravity

T. Banks and N. Seiberg,Symmetries and Strings in Field Theory and Gravity,Phys. Rev. D83(2011) 084019, [1011.5120]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[4]

S.-J. Lee, W. Lerche and T. Weigand,Tensionless Strings and the Weak Gravity Conjecture,JHEP10(2018) 164, [1808.05958]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[5]

S.-J. Lee, W. Lerche and T. Weigand,A Stringy Test of the Scalar Weak Gravity Conjecture,Nucl. Phys. B938(2019) 321–350, [1810.05169]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[6]

H.-C. Kim, G. Shiu and C. Vafa,Branes and the Swampland,Phys. Rev. D100 (2019) 066006, [1905.08261]

work page arXiv 2019
[7]

Kim, H.-C

H.-C. Kim, H.-C. Tarazi and C. Vafa,Four-dimensionalN=4SYM theory and the swampland,Phys. Rev. D102(2020) 026003, [1912.06144]

work page arXiv 2020
[8]

Katz, H.-C

S. Katz, H.-C. Kim, H.-C. Tarazi and C. Vafa,Swampland Constraints on 5dN= 1 Supergravity,JHEP07(2020) 080, [2004.14401]

work page arXiv 2020
[9]

Angelantonj, Q

C. Angelantonj, Q. Bonnefoy, C. Condeescu and E. Dudas,String Defects, Supersymmetry and the Swampland,JHEP11(2020) 125, [2007.12722]

work page arXiv 2020
[10]

Tarazi and C

H.-C. Tarazi and C. Vafa,On The Finiteness of 6d Supergravity Landscape, 2106.10839

work page arXiv
[11]

Hamada and G

Y. Hamada and G. J. Loges,Enumerating 6D supergravities with T≤1,JHEP12 (2024) 167, [2404.08845]

work page arXiv 2024
[12]

H.-C. Kim, C. Vafa and K. Xu,Finite landscape of 6d N=(1,0) supergravity,SciPost Phys.20(2026) 016, [2411.19155]

work page arXiv 2026
[13]

Hamada and G

Y. Hamada and G. J. Loges,A finite 6d supergravity landscape from anomalies, 2507.20949

work page arXiv
[14]

Hamada and C

Y. Hamada and C. Vafa,8d supergravity, reconstruction of internal geometry and the Swampland,JHEP06(2021) 178, [2104.05724]

work page arXiv 2021
[15]

Bedroya, Y

A. Bedroya, Y. Hamada, M. Montero and C. Vafa,Compactness of brane moduli and the String Lamppost Principle in d>6,JHEP02(2022) 082, [2110.10157]

work page arXiv 2022
[16]

Lockhart and L

G. Lockhart and L. Novelli,The hyperplane string, RCFTs, and the swampland, JHEP11(2025) 065, [2506.05173]

work page arXiv 2025
[17]

Lockhart and Y

G. Lockhart and Y. Proto,Rational points in the 6d supergravity landscape and simple current extensions,2603.17713. – 78 –

work page arXiv
[18]

O. J. Ganor and A. Hanany,Small E(8) instantons and tensionless noncritical strings,Nucl. Phys. B474(1996) 122–140, [hep-th/9602120]

work page internal anchor Pith review Pith/arXiv arXiv 1996
[19]

Comments on String Dynamics in Six Dimensions

N. Seiberg and E. Witten,Comments on string dynamics in six-dimensions,Nucl. Phys. B471(1996) 121–134, [hep-th/9603003]

work page internal anchor Pith review Pith/arXiv arXiv 1996
[20]

BPS States of Exceptional Non-Critical Strings

A. Klemm, P. Mayr and C. Vafa,BPS states of exceptional noncritical strings,Nucl. Phys. B Proc. Suppl.58(1997) 177, [hep-th/9607139]

work page internal anchor Pith review Pith/arXiv arXiv 1997
[21]

M-Strings

B. Haghighat, A. Iqbal, C. Koz¸ caz, G. Lockhart and C. Vafa,M-Strings,Commun. Math. Phys.334(2015) 779–842, [1305.6322]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[22]

Z. K. Baykara, Y. Hamada, H.-C. Tarazi and C. Vafa,On the string landscape without hypermultiplets,JHEP04(2024) 121, [2309.15152]

work page arXiv 2024
[23]

Z. K. Baykara, H.-C. Tarazi and C. Vafa,Quasicrystalline string landscape,Phys. Rev. D111(2025) 086025, [2406.00129]

work page arXiv 2025
[24]

Kim and C

H.-C. Kim and C. Vafa,Exploring new constraints on K¨ ahler moduli space of 6dN= 1 supergravity,JHEP10(2024) 217, [2406.06704]

work page arXiv 2024
[25]

Heidenreich, M

B. Heidenreich, M. Reece and T. Rudelius,The Weak Gravity Conjecture and axion strings,JHEP11(2021) 004, [2108.11383]

work page arXiv 2021
[26]

Theta-problem and the String Swampland

S. Cecotti and C. Vafa,Theta-problem and the String Swampland,1808.03483

work page internal anchor Pith review Pith/arXiv arXiv
[27]

Gravitational Anomaly Cancellation for M-Theory Fivebranes

D. Freed, J. A. Harvey, R. Minasian and G. W. Moore,Gravitational anomaly cancellation for M theory five-branes,Adv. Theor. Math. Phys.2(1998) 601–618, [hep-th/9803205]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[28]

J. A. Harvey, R. Minasian and G. W. Moore,NonAbelian tensor multiplet anomalies, JHEP09(1998) 004, [hep-th/9808060]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[29]

D-brane anomaly inflow revisited

H. Kim and P. Yi,D-brane anomaly inflow revisited,JHEP02(2012) 012, [1201.0762]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[30]

P.-S. Hsin, H. T. Lam and N. Seiberg,Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d,SciPost Phys.6(2019) 039, [1812.04716]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[31]

A. Font, L. E. Ibanez and F. Quevedo,Higher Level Kac-Moody String Models and Their Phenomenological Implications,Nucl. Phys. B345(1990) 389–430

work page 1990
[32]

Kaufmann, S

L. Kaufmann, S. Lanza and T. Weigand,Asymptotics of 5d supergravity theories and the emergent string conjecture,JHEP06(2025) 230, [2412.12251]

work page arXiv 2025
[33]

S.-J. Lee, W. Lerche and T. Weigand,Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions,JHEP08(2019) 104, [1901.08065]

work page arXiv 2019
[34]

S.-J. Lee, W. Lerche, G. Lockhart and T. Weigand,Quasi-Jacobi forms, elliptic genera and strings in four dimensions,JHEP01(2021) 162, [2005.10837]. – 79 –

work page arXiv 2021
[35]

Xu,On TCS G 2 manifolds and 4D emergent strings,JHEP10(2020) 045 [2006.02350]

F. Xu,On TCS G 2 manifolds and 4D emergent strings,JHEP10(2020) 045, [2006.02350]

work page arXiv 2020
[36]

Grieco, I

A. Grieco, I. Ruiz and I. Valenzuela,EFT strings and dualities in 4dN= 1, 2504.16984

work page arXiv
[37]

G. F. Casas and M. Wiesner,Towards the Non-Perturbative Completion of 4d N=1 Effective Theories of Gravity,2510.23698

work page arXiv
[38]

F-Theory, Spinning Black Holes and Multi-string Branches

B. Haghighat, S. Murthy, C. Vafa and S. Vandoren,F-theory, spinning black holes and multi-string branches,1509.00455

work page internal anchor Pith review Pith/arXiv arXiv
[39]

Universal Features of BPS Strings in Six-dimensional SCFTs

M. Del Zotto and G. Lockhart,Universal Features of BPS Strings in Six-dimensional SCFTs,JHEP08(2018) 173, [1804.09694]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[40]

A. N. Schellekens and S. Yankielowicz,Extended Chiral Algebras and Modular Invariant Partition Functions,Nucl. Phys. B327(1989) 673–703

work page 1989
[41]

A. N. Schellekens and S. Yankielowicz,Simple Currents, Modular Invariants and Fixed Points,Int. J. Mod. Phys. A5(1990) 2903–2952

work page 1990
[42]

A. N. Schellekens and S. Yankielowicz,Modular Invariants From Simple Currents: An Explicit Proof,Phys. Lett. B227(1989) 387–391

work page 1989
[43]

K. A. Intriligator,Bonus Symmetry in Conformal Field Theory,Nucl. Phys. B332 (1990) 541–565

work page 1990
[44]

Fuchs,Simple WZW currents,Commun

J. Fuchs,Simple WZW currents,Commun. Math. Phys.136(1991) 345–356

work page 1991
[45]

Di Francesco, P

P. Di Francesco, P. Mathieu and D. Senechal,Conformal Field Theory. Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997, 10.1007/978-1-4612-2256-9

work page doi:10.1007/978-1-4612-2256-9 1997
[46]

I. V. Melnikov,An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry, vol. 951 ofLecture Notes in Physics. Springer, 2019, 10.1007/978-3-030-05085-6

work page doi:10.1007/978-3-030-05085-6 2019
[47]

Coupling a QFT to a TQFT and Duality

A. Kapustin and N. Seiberg,Coupling a QFT to a TQFT and Duality,JHEP04 (2014) 001, [1401.0740]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[48]

Generalized Global Symmetries

D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett,Generalized Global Symmetries, JHEP02(2015) 172, [1412.5148]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[49]

Symmetries in quantum field theory and quantum gravity

D. Harlow and H. Ooguri,Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys.383(2021) 1669–1804, [1810.05338]

work page internal anchor Pith review Pith/arXiv arXiv 2021
[50]

Aharony, N

O. Aharony, N. Seiberg and Y. Tachikawa,Reading between the lines of four-dimensional gauge theories,JHEP08(2013) 115, [1305.0318]

work page arXiv 2013
[51]

Córdova, D

C. C´ ordova, D. S. Freed, H. T. Lam and N. Seiberg,Anomalies in the Space of – 80 – Coupling Constants and Their Dynamical Applications II,SciPost Phys.8(2020) 002, [1905.13361]

work page arXiv 2020
[52]

Apruzzi, M

F. Apruzzi, M. Dierigl and L. Lin,The fate of discrete 1-form symmetries in 6d, SciPost Phys.12(2022) 047, [2008.09117]

work page arXiv 2022
[53]

Cvetiˇ c, M

M. Cvetiˇ c, M. Dierigl, L. Lin and H. Y. Zhang,String Universality and Non-Simply-Connected Gauge Groups in 8d,Phys. Rev. Lett.125(2020) 211602, [2008.10605]

work page arXiv 2020
[54]

Benetti Genolini and L

P. Benetti Genolini and L. Tizzano,Instantons, symmetries and anomalies in five dimensions,JHEP04(2021) 188, [2009.07873]

work page arXiv 2021
[55]

A. Font, B. Fraiman, M. Gra˜ na, C. A. N´ u˜ nez and H. Parra De Freitas,Exploring the landscape of CHL strings on T d,JHEP08(2021) 095, [2104.07131]

work page arXiv 2021
[56]

Cvetic, M

M. Cvetic, M. Dierigl, L. Lin and H. Y. Zhang,Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacua,Phys. Rev. D104(2021) 086018, [2107.04031]

work page arXiv 2021
[57]

Hsieh, Y

C.-T. Hsieh, Y. Tachikawa and K. Yonekura,Anomaly Inflow and p-Form Gauge Theories,Commun. Math. Phys.391(2022) 495–608, [2003.11550]

work page arXiv 2022
[58]

G. W. Moore and N. Seiberg,Naturality in Conformal Field Theory,Nucl. Phys. B 313(1989) 16–40

work page 1989
[59]

G. W. Moore and N. Seiberg,Taming the Conformal Zoo,Phys. Lett. B220(1989) 422–430

work page 1989
[60]

D. R. Morrison and W. Taylor,Classifying bases for 6D F-theory models,Central Eur. J. Phys.10(2012) 1072–1088, [1201.1943]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[61]

J. J. Heckman, D. R. Morrison, T. Rudelius and C. Vafa,Atomic Classification of 6D SCFTs,Fortsch. Phys.63(2015) 468–530, [1502.05405]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[62]

Dierigl, P.-K

M. Dierigl, P.-K. Oehlmann and F. Ruehle,Non-Simply-Connected Symmetries in 6D SCFTs,JHEP10(2020) 173, [2005.12929]

work page arXiv 2020
[63]

The Global Gauge Group Structure of F-theory Compactification with U(1)s

M. Cvetic and L. Lin,The Global Gauge Group Structure of F-theory Compactification with U(1)s,JHEP01(2018) 157, [1706.08521]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[64]

TASI Lectures on Abelian and Discrete Symmetries in F-theory

M. Cvetiˇ c and L. Lin,TASI Lectures on Abelian and Discrete Symmetries in F-theory,PoST ASI2017(2018) 020, [1809.00012]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[65]

P. S. Aspinwall and D. R. Morrison,Nonsimply connected gauge groups and rational points on elliptic curves,JHEP07(1998) 012, [hep-th/9805206]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[66]

D. R. Morrison and D. S. Park,F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds,JHEP10(2012) 128, [1208.2695]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[67]

Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory

C. Mayrhofer, D. R. Morrison, O. Till and T. Weigand,Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory,JHEP10(2014) 016, [1405.3656]. – 81 –

work page internal anchor Pith review Pith/arXiv arXiv 2014
[68]

Shioda,Mordell-Weil lattices and Galois representation, I,Proceedings of the Japan Academy, Series A, Mathematical Sciences65(1989) 268 – 271

T. Shioda,Mordell-Weil lattices and Galois representation, I,Proceedings of the Japan Academy, Series A, Mathematical Sciences65(1989) 268 – 271

work page 1989
[69]

Shioda,On the Mordell-Weil Lattices,Commentarii Mathematici Universitatis Sancti Pauli39(01, 1990)

T. Shioda,On the Mordell-Weil Lattices,Commentarii Mathematici Universitatis Sancti Pauli39(01, 1990)

work page 1990
[70]

Miranda and U

R. Miranda and U. Persson,Configurations of Infibers on elliptic K 3 surfaces, Mathematische Zeitschrift201(Sept., 1989) 339–361

work page 1989
[71]

Toroidal Compactification Without Vector Structure

E. Witten,Toroidal compactification without vector structure,JHEP02(1998) 006, [hep-th/9712028]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[72]

K. S. Narain, M. H. Sarmadi and C. Vafa,Asymmetric Orbifolds,Nucl. Phys. B288 (1987) 551

work page 1987
[73]

Bianchi, G

M. Bianchi, G. Bossard and D. Consoli,Perturbative higher-derivative terms inN= 6 asymmetric orbifolds,JHEP06(2022) 088, [2203.15130]

work page arXiv 2022
[74]

B. S. Acharya, G. Aldazabal, A. Font, K. Narain and I. G. Zadeh,Heterotic strings onT 3/Z2, Nikulin involutions and M-theory,JHEP09(2022) 209, [2205.09764]

work page arXiv 2022
[75]

Fraiman and H

B. Fraiman and H. Parra De Freitas,Unifying the 6DN= (1, 1) string landscape, JHEP02(2023) 204, [2209.06214]

work page arXiv 2023
[76]

Gkountoumis, C

G. Gkountoumis, C. Hull, K. Stemerdink and S. Vandoren,Freely acting orbifolds of type IIB string theory on T 5,JHEP08(2023) 089, [2302.09112]

work page arXiv 2023
[77]

A. E. Faraggi, S. Groot Nibbelink and B. Percival,Free fermionic webs of heterotic T folds,Phys. Rev. D109(2024) L051701, [2306.16443]

work page arXiv 2024
[78]

Gkountoumis, C

G. Gkountoumis, C. Hull and S. Vandoren,Exact moduli spaces forN= 2, D = 5 freely acting orbifolds,JHEP07(2024) 126, [2403.05650]

work page arXiv 2024
[79]

Z. K. Baykara, H.-C. Tarazi and C. Vafa,New Nonsupersymmetric Tachyon-Free Strings,Phys. Rev. Lett.136(2026) 061602, [2406.00185]

work page arXiv 2026
[80]

Angelantonj, I

C. Angelantonj, I. Florakis, G. Leone and D. Perugini,Non-supersymmetric non-tachyonic heterotic vacua with reduced rank in various dimensions,JHEP10 (2024) 216, [2407.09597]

work page arXiv 2024

Showing first 80 references.