Schwinger-Type Pair Production in Non-SUSY AdS/CFT

<div>The figure on the left illustrates relation between the pair production rate and applied electric field for pure <svg height="9.25986pt" id="M349" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -9.01432 33.9437 9.25986" width="33.9437pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M569 131C584 203 591 291 596 391C603 524 609 615 622 658L609 669C545 642 461 523 357 312C267 129 194 14 119 14C104 14 91 21 88 36H91C96 33 101 32 107 32C134 32 149 54 149 77C149 104 128 128 97 128C65 128 38 101 38 62C38 19 71 -15 118 -15C207 -15 274 84 391 315C446 423 501 518 534 563L535 562C518 501 511 401 508 297C504 160 495 63 476 -13H496C588 65 656 224 712 363C783 536 828 621 863 640H866C866 608 894 595 913 595C937 595 956 613 956 641C956 670 935 687 904 687C875 687 853 675 830 650C782 596 735 496 692 394C649 290 605 184 570 131H569Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.242,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.505,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g></svg> SYM (<a href="https://static.hindawi.com/articles/ahep/volume-2023/8685867/figures/#EEq44">78</a>). In our units, the critical electric field is at <span class="nowrap"><svg height="12.5794pt" id="M350" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 46.9646 12.5794" width="46.9646pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M421 658C372 683 338 687 289 687C174 687 100 624 100 549C100 458 196 404 336 401C341 401 342 386 347 381V379C196 347 110 258 110 154C110 43 211 -15 326 -15C463 -15 584 71 584 161C584 228 542 276 450 276C352 276 275 206 248 98L269 92C293 177 364 234 433 234C485 234 520 207 520 160C520 131 509 102 485 75C454 40 404 15 336 15C244 15 192 73 192 134C192 220 267 311 387 343C403 334 419 329 440 329C464 329 482 338 482 357C482 377 454 385 407 388C404 392 404 393 403 400C588 413 734 506 734 585C734 633 698 658 634 658C511 658 343 568 332 432C229 432 141 472 141 546C141 610 204 657 301 657C356 657 372 656 411 640L421 658ZM693 588C693 524 566 441 403 430C416 521 546 621 641 621C670 621 693 608 693 588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.75,3.132)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.634,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.897,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.137,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.498,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg>.</span> The right figure is for non-supersymmetric case (<a href="https://static.hindawi.com/articles/ahep/volume-2023/8685867/figures/#EEq43">77</a>) for the value <span class="nowrap"><svg height="9.63826pt" id="M351" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -9.28833 51.1941 9.63826" width="51.1941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.354,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.617,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.248,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.488,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.452,0)"><path d="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.694,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g></svg>.</span> Almost no change in the profile is found.</div>

Advances in High Energy Physics

Schwinger-Type Pair Production in Non-SUSY AdS/CFT

Figure 6